JEE Main & Advanced Physics Wave Mechanics Question Bank

done Self Evaluation Test - Waves Total Questions - 85

• question_answer1)
  When two sound waves travel in the same direction in a medium, the displacements of a particle located at 'x' at time 't' is given by: \[{{y}_{1}}=0.05\cos (0.50\pi x-100\pi t)\] \[{{y}_{2}}=0.05\cos (0.46\pi x-92\pi t)\] Where\[{{y}_{1}}\] , \[{{y}_{2}}\] and x are in meters and t seconds. The speed of sound in the medium is:
  A)
  92m/s done clear
  B)
  200 m/s done clear
  C)
  100m/s done clear
  D)
  332m/s done clear
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• question_answer2)
  The extension in a string, obeying Hooke's law, is x. The speed of sound in the stretched string is v. If the extension in the string is increased to 1.5x, the speed of sound will be
  A)
   1.22v done clear
  B)
   0.61v done clear
  C)
  1.50v done clear
  D)
  0.75v done clear
  View Solution play_arrow

• question_answer3)
  A wave travelling on a string is described by \[y=(x,t)=0.005\,\sin \,(80.0x-3.0t)\] The period of the wave is
  A)
   3.00 s done clear
  B)
   2.09 s done clear
  C)
  0.48 s done clear
  D)
  0.05 s done clear
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• question_answer4)
  A closed organ pipe (closed at one end) is excited to support the third overtone. It is found that air in the pipe has          
  A)
   three nodes and three antinodes done clear
  B)
   three nodes and four antinodes done clear
  C)
  four nodes and three antinodes done clear
  D)
  four nodes and four antinodes done clear
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• question_answer5)
  If there are six loops for 1 m length in transverse mode of Melde's experiment., the no. of loops in longitudinal mode under otherwise identical conditions would be
  A)
   3 done clear
  B)
   6     done clear
  C)
  12 done clear
  D)
  8 done clear
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• question_answer6)
  If\[{{n}_{1}}\],\[{{n}_{2}}\]and \[{{n}_{3}}\] are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by    
  A)
   \[\frac{1}{n}=\frac{1}{{{n}_{1}}}+\frac{1}{{{n}_{2}}}+\frac{1}{{{n}_{3}}}\] done clear
  B)
   \[\frac{1}{\sqrt{n}}=\frac{1}{\sqrt{{{n}_{1}}}}+\frac{1}{\sqrt{{{n}_{2}}}}+\frac{1}{\sqrt{{{n}_{3}}}}\] done clear
  C)
  \[\sqrt{n}=\sqrt{{{n}_{1}}}+\sqrt{{{n}_{2}}}+\sqrt{{{n}_{3}}}\] done clear
  D)
  \[n={{n}_{1}}+{{n}_{2}}+{{n}_{3}}\] done clear
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• question_answer7)
  When a sound wave goes from one medium to another, the quantity that remains unchanged is
  A)
   frequency done clear
  B)
   amplitude done clear
  C)
  wavelength done clear
  D)
  speed done clear
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• question_answer8)
  Of the following, the equation of plane progressive wave is
  A)
   \[y=r\sin \,\omega t\] done clear
  B)
   \[y=r\sin (\omega t-kx)\] done clear
  C)
  \[y=\frac{a}{\sqrt{r}}\sin (\omega t-kx)\] done clear
  D)
  \[y=\frac{a}{r}\sin (\omega t-kr)\] done clear
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• question_answer9)
  Consider the three waves \[{{z}_{1}}\], \[{{z}_{2}}\] and \[{{z}_{3}}\] as \[{{z}_{1}}=A\,\sin (kx-\omega t);\,\,\,{{z}_{2}}=A\,\sin (kx+\omega t)\] \[{{z}_{3}}=A\sin (ky-\omega t)\] Which of the following represents a standing wave?
  A)
   \[{{z}_{1}}+{{z}_{2}}\] done clear
  B)
   \[{{z}_{2}}+{{z}_{3}}\] done clear
  C)
  \[{{z}_{3}}+{{z}_{1}}\] done clear
  D)
  \[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}\]   done clear
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• question_answer10)
  Two waves are represented by the equations \[{{y}_{1}}=a\sin (\omega t+kx+0.57)m\] and \[{{y}_{2}}=a\cos \]\[(\omega t+kx)m\], where x is in meter and t in sec. The phase difference between them is
  A)
   1.0 radian        done clear
  B)
          1.25 radian done clear
  C)
  1.57 radian       done clear
  D)
         0.57 radian done clear
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• question_answer11)
  A transverse wave is represented by\[y=A\sin (\omega t+kx)\]. For what value of the wavelength is the wave velocity equal to the maximum particle velocity?
  A)
   \[\frac{\pi A}{2}\]                     done clear
  B)
   \[\pi A\] done clear
  C)
  \[2\pi A\]            done clear
  D)
  \[A\] done clear
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• question_answer12)
  The displacement y of a particle in a medium can be expressed as, \[y={{10}^{-6}}\sin \left( 100t+20x+\frac{\pi }{4} \right)m\] where t is in second and x in meter. The speed of the wave is
  A)
   \[20m/s\]           done clear
  B)
          \[5m/s\]   done clear
  C)
  \[2000m/s\]        done clear
  D)
         \[~57m/s\]   done clear
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• question_answer13)
  A progressive sound wave of frequency 500 Hz is travelling through air with a speed of \[350m{{s}^{-1}}\]. A compression maximum appears at a place at a given instant. The minimum time interval after which the rare fraction maximum occurs at the same point, is
  A)
   \[200s\] done clear
  B)
   \[\frac{1}{250}s\] done clear
  C)
  \[\frac{1}{500}s\] done clear
  D)
  \[\frac{1}{1000}s\] done clear
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• question_answer14)
  At t=0, the shape of a travelling pulse is given by \[y(x,0)=\frac{4\times {{10}^{-3}}}{8\times {{(x)}^{-2}}}\] where x and y are in metres. The wave function for the travelling pulse if the velocity or propagation is 5 m/s in the x direction is given by
  A)
   \[y(x,t)=\frac{4\times {{10}^{-3}}}{8-({{x}^{2}}-5t)}\] done clear
  B)
   \[y(x,t)=\frac{4\times {{10}^{-3}}}{8-{{(x-5t)}^{2}}}\] done clear
  C)
  \[y(x,t)=\frac{4\times {{10}^{-3}}}{8-{{(x+5t)}^{2}}}\] done clear
  D)
  \[y(x,t)=\frac{4\times {{10}^{-3}}}{8-({{x}^{2}}+5t)}\] done clear
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• question_answer15)
  A plane progressive simple harmonic sound wave of angular frequency \[680\text{ }rad/s\] moves with speed 340 m/s in the direction which makes equal angle with each x, y and z-axis. The phase difference (\[{{\phi }_{1}}-{{\phi }_{2}}\]) between the oscillations of the particle in the medium located at the positions \[(\sqrt{3,}\sqrt{3,}\sqrt{3})\]and \[(2\sqrt{3,}\,2\sqrt{3,}\,2\sqrt{3})\] is (assume\[\cos \theta >0\])
  A)
   2 radian done clear
  B)
   3 radian done clear
  C)
  4 radian done clear
  D)
  6 radian done clear
  View Solution play_arrow

• question_answer16)
  The amplitude of a wave disturbance propagating in the positive x-direction is given by \[y=\frac{1}{1+{{x}^{2}}}\] at t=0 and \[y=\frac{1}{2+{{x}^{2}}-2x}\] at t = 2s, where x and y are in meter. Assuming that the shape of the wave disturbance does not change during the propagation, the speed of the wave is
  A)
   \[0.5m/s\]          done clear
  B)
   \[~1m/s\] done clear
  C)
  \[1.5m/s\]           done clear
  D)
  \[2\text{ }m/s\] done clear
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• question_answer17)
  A small piece of cork in a ripple tank oscillates up and down as ripple pass it. If the ripples travelling at 0.3 m/s have a wavelength of \[1.5\pi \,cm\] and the cork vibrates with an amplitude of \[5\,\,mm,\] the maximum velocity of the cork is:  
  A)
   \[20\text{ }cm/sec\] done clear
  B)
   \[20m/sec\] done clear
  C)
  \[0.02m/sec~\] done clear
  D)
  \[~200\text{ }cm/sec\] done clear
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• question_answer18)
  The wave described by y =0.25 sin \[(10\pi x-2\pi t),\]where x and y are in meters and t in seconds, is a wave travelling along the:     
  A)
   \[-ve\]x direction with frequency 1 Hz. done clear
  B)
   \[+ve\]x direction with frequency n Hz and wavelength \[\lambda =0.2m\]. done clear
  C)
  \[+ve\] x direction with frequency 1 Hz and wavelength \[\lambda =0.2m\] done clear
  D)
  \[-ve\] x direction with amplitude 0.25 m and wavelength \[\lambda =0.2m\] done clear
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• question_answer19)
  When a longitudinal wave propagates through a medium, the particles of the medium execute simple harmonic oscillations about their mean positions. These oscillations of a particle are characterized by an invariant
  A)
   kinetic energy done clear
  B)
   potential energy done clear
  C)
  sum of kinetic energy and potential energy done clear
  D)
  difference between kinetic energy and potential energy done clear
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• question_answer20)
  In a transverse wave the distance between a crest and neighboring trough at the same instant is 4.0 cm and the distance between a crest and trough at the same place is 1.0 cm. The next crest appears at the same place after a time interval of 0.4s.The maximum speed of the vibrating particles in the medium is:
  A)
   \[\frac{3\pi }{2}cm/s\] done clear
  B)
   \[\frac{5\pi }{2}cm/s\] done clear
  C)
  \[\frac{\pi }{2}cm/s\] done clear
  D)
  \[2\pi cm/s\] done clear
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• question_answer21)
  An earthquake generates both transverse (5) and longitudinal (P) sound waves in the earth. The speed of S waves in about 4.5 km/s and that of waves is about 8.0 km/s. A seismograph records P and S waves from an earthquake. The first P wave arrives 4.0 min. before the first 5'wave. The epicenter of the earthquake is located at a distance about           
  A)
   25 km done clear
  B)
   250 km done clear
  C)
  2500 km done clear
  D)
  5000 km done clear
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• question_answer22)
  A progressive wave is travelling in a medium such that frequency of oscillation and displacement amplitude of the particles of the medium are/and A respectively. The ratio of their acceleration amplitude and velocity amplitude is
  A)
   \[2\pi f\] done clear
  B)
   \[\pi f\]    done clear
  C)
  \[\frac{2\pi f}{A}\] done clear
  D)
  \[\frac{\pi f}{A}\] done clear
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• question_answer23)
  In a plane progressive harmonic wave particle speed is always less than the wave speed if
  A)
   amplitude of wave is less than \[\frac{\lambda }{2\pi }\] done clear
  B)
   amplitude of wave is greater than\[\frac{\lambda }{2\pi }\] done clear
  C)
  amplitude of wave is less than \[\lambda \] done clear
  D)
  amplitude of wave is greater than\[\frac{\lambda }{\pi }\] done clear
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• question_answer24)
  Equation of a progressive wave is given by \[y=4\sin \left[ \pi \left( \frac{1}{5}-\frac{x}{9} \right)+\frac{\pi }{6} \right]\] Then which of the following is correct?
  A)
   v = 5cm done clear
  B)
   \[\lambda =18cm\] done clear
  C)
  a = 0.04 cm done clear
  D)
  f=50Hz done clear
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• question_answer25)
  A transverse sinusoidal wave, moves along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time t, the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is  
  A)
   \[\frac{\sqrt{3\pi }}{50}\hat{j}m/s\] done clear
  B)
   \[-\frac{\sqrt{3\pi }}{50}\hat{j}m/s\] done clear
  C)
  \[\frac{\sqrt{3\pi }}{50}\hat{i}m/s\] done clear
  D)
  \[-\frac{\sqrt{3\pi }}{50}\hat{i}m/s\] done clear
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• question_answer26)
  Sound waves are travelling in a medium whose adiabatic elasticity is E and isothermal elasticity E'. The velocity of sound waves is proportional to
  A)
   \[E'\] done clear
  B)
   \[\sqrt{E}\]  done clear
  C)
  \[\sqrt{E'}\] done clear
  D)
  \[\frac{E}{E'}\] done clear
  View Solution play_arrow

• question_answer27)
  What is the effect of humidity on sound waves when humidity increases?
  A)
   Speed of sound waves is more done clear
  B)
   Speed of sound waves is less done clear
  C)
  Speed of sound waves remains same done clear
  D)
  Speed of sound waves becomes zero done clear
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• question_answer28)
  The bulk modulus of a liquid of density 8000 kg\[8000kg\,{{m}^{-3}}\]is \[2\times {{10}^{9}}N\,{{m}^{-2}}\]. The speed of sound in that liquid is (\[in\,m\,{{s}^{-1}}\])  
  A)
   200 done clear
  B)
   250   done clear
  C)
  100 done clear
  D)
  500 done clear
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• question_answer29)
  The velocity of sound in hydrogen is\[1224\text{ }m/s\]. Its velocity in a mixture of hydrogen and oxygen containing 4 parts by volume of hydrogen and 1 part oxygen is   
  A)
   \[1224\text{ }m/s~\] done clear
  B)
   \[612\text{ }m/s\] done clear
  C)
  \[2448\text{ }m/s~\] done clear
  D)
  \[306\text{ }m/s\] done clear
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• question_answer30)
  When a sound wave of frequency 300 Hz passes through a medium, the maximum displacement of a particle of the medium is 0.1 cm. The maximum velocity of the particle is equal to
  A)
   \[60\pi c{{m}^{-1}}\] done clear
  B)
   \[30\pi c{{m}^{-1}}\] done clear
  C)
  \[30cm{{s}^{-1}}\] done clear
  D)
  \[60cm{{s}^{-1}}\] done clear
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• question_answer31)
  Velocity of sound waves in air is 330 m/s. For a particular sound wave in air, a path difference of 40 cm is equivalent to phase difference of 1.671. The frequency of this wave is
  A)
   \[165\text{ }Hz\] done clear
  B)
   \[150\text{ }Hz\] done clear
  C)
  \[60{}^\circ \] done clear
  D)
  \[330\,Hz\] done clear
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• question_answer32)
  A hospital uses an ultrasonic scanner to locate tumours in a tissue. The operating frequency of the scanner is 4.2 MHz. The speed of sound in a tissue is 1.7 km/s. The wavelength of sound in tissue is close to
  A)
   \[4\times {{10}^{-4}}m\] done clear
  B)
   \[8\times {{10}^{-4}}m\] done clear
  C)
  \[4\times {{10}^{-3}}m\] done clear
  D)
  \[8\times {{10}^{-3}}m\]   done clear
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• question_answer33)
  A person speaking normally produces a sound intensity of 40 dB at a distance of 1 m. If the threshold intensity for reasonable audibility is 20 dB, the maximum distance at which he can be heard clearly is
  A)
   \[4m\] done clear
  B)
   \[~5m\]   done clear
  C)
  \[10m\]  done clear
  D)
  \[20m\] done clear
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• question_answer34)
  The fundamental frequency of a closed end organ pipe is n. Its length is doubled and radius is halved. Its frequency will become nearly
  A)
   \[n/2\] done clear
  B)
   \[n/3\] done clear
  C)
  n done clear
  D)
  \[2n\] done clear
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• question_answer35)
  The fundamental frequency of an organ pipe is 512 Hz. If its length is increased, then frequency will
  A)
   decrease done clear
  B)
   increase done clear
  C)
  remains same done clear
  D)
  cannot be predicted done clear
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• question_answer36)
  Tube A has both ends open while tube B has one end closed, otherwise they are identical. The ratio of fundamental frequency of tube A and B is
  A)
   1 : 2 done clear
  B)
   1 : 4 done clear
  C)
  2 : 1 done clear
  D)
  4 : 1 done clear
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• question_answer37)
  If the length of a stretched string is shortened by 40% and the tension increased by 44% then the ratio of the final and initial fundamental frequencies is            
  A)
   3 : 4 done clear
  B)
   4 : 3  done clear
  C)
  1 : 3 done clear
  D)
  2 : 1 done clear
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• question_answer38)
  The number of possible natural oscillation of air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are: (velocity of sound \[=340m{{s}^{-1}}\])
  A)
   4 done clear
  B)
   5       done clear
  C)
  7 done clear
  D)
  6 done clear
  View Solution play_arrow

• question_answer39)
  The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is
  A)
   100 cm done clear
  B)
   120 cm done clear
  C)
  140 cm done clear
  D)
  80 cm done clear
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• question_answer40)
  Two strings A and B, made of same material, are stretched by same tension. The radius of string A is double of radius of B. A transverse wave travels on A with speed \[{{V}_{A}}\]and on B with speed Vo. The ratio \[{{V}_{A}}/{{V}_{B}}\]is
  A)
   1/2       done clear
  B)
   2     done clear
  C)
  1/4                    done clear
  D)
  4 done clear
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• question_answer41)
    In the sonometer experiment, a tuning fork of frequency 256 Hz is in resonance with 0.4 m length of the wire when the iron load attached to free end of wire is 2 kg. If the load is immersed in water, the length of the wire in resonance would be (specific gravity of iron = 8) 4
  A)
   0.37 m done clear
  B)
   0.43 m done clear
  C)
  0.31 m done clear
  D)
  0.2 m done clear
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• question_answer42)
  Two identical piano wires kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beats/s when both the wires oscillate together would be
  A)
   0.02  done clear
  B)
   0.03   done clear
  C)
  0.04  done clear
  D)
  0.01 done clear
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• question_answer43)
  The length of the wire between two ends of asonometer is 100 cm. What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio of 1 : 3 : 5?
  A)
   \[\frac{1500}{23}cm,\frac{2000}{23}cm\] done clear
  B)
   \[\frac{1500}{23}cm,\frac{500}{23}cm\] done clear
  C)
  \[\frac{1500}{23}cm,\frac{300}{23}cm\] done clear
  D)
  \[\frac{300}{23}cm,\frac{1500}{23}cm\]   done clear
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• question_answer44)
  An organ pipe \[{{P}_{1}}\] closed at one end vibrating in its first overtone and another pipe \[{{P}_{2}}\] open at both ends vibrating in third overtone are in resonance with a given tuning fork. The ratio of the length of \[{{P}_{1}}\] to that of \[{{P}_{2}}\] is
  A)
   8/3 done clear
  B)
   3/8   done clear
  C)
  ½ done clear
  D)
  1/3 done clear
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• question_answer45)
  Length of a sonometer wire between two fixed ends is 110 cm. If the fundamental frequencies are in the ratio of 1: 2: 3, then what is the ratio of lengths of these segments of the wire?
  A)
   3 : 2 : 1 done clear
  B)
   6 : 3 : 2 done clear
  C)
  6 : 2 : 3 done clear
  D)
  2 : 3 : 6 done clear
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• question_answer46)
  The equation of a wave on a string of linear mass density \[0.04kg\,{{m}^{-1}}\] is given by \[y=0.02(m)\sin \left[ 2\pi \left( \frac{1}{0.04(s)}-\frac{x}{0.50(m)} \right) \right]\] The tension in the string is
  A)
   4.0 N done clear
  B)
   12.5 N done clear
  C)
  0.5 N done clear
  D)
  6.25 N done clear
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• question_answer47)
  A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are \[7.7\times {{10}^{3}}kg/{{m}^{3}}\] and \[2.2\times {{10}^{11}}N/{{m}^{2}}\] respectively?
  A)
   188.5 Hz done clear
  B)
   178.2 Hz done clear
  C)
  200.5 Hz done clear
  D)
  770 Hz done clear
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• question_answer48)
  A sonometer wire supports a 4 kg load and vibrates in fundamental mode with a tuning fork of frequency 416 Hz. The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to
  A)
   1 kg     done clear
  B)
   2 kg done clear
  C)
  4 kg      done clear
  D)
  16 kg done clear
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• question_answer49)
  Two pulses in a stretched string whose centres are initially 8 cm apart are moving towards each other as shown in the figure. The speed of each pulse is 2 cm/s. After 2 s, the total energy of the pulses will be
  A)
   Zero                done clear
  B)
   Purely kinetic         done clear
  C)
         Purely potential    done clear
  D)
    Partly kinetic and partly potential done clear
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• question_answer50)
  A stretched wire 60 cm long is vibrating with its fundamental frequency of 256 Hz. If the length of the wire is decreased to 15 cm and the tension remains the same. Then the fundamental freuqency of the vibration of the wire will be
  A)
   1024    done clear
  B)
   572   done clear
  C)
  256       done clear
  D)
  64 done clear
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• question_answer51)
  A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is
  A)
   105 Hz           done clear
  B)
          1.05 Hz done clear
  C)
  1050 Hz          done clear
  D)
         10.5 Hz done clear
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• question_answer52)
  The fundamental frequency of an open organ pipe is 300 Hz. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is 330 m/s, then the length of closed organ pipe is
  A)
   41cm done clear
  B)
   37cm done clear
  C)
  31cm done clear
  D)
  80cm done clear
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• question_answer53)
  In a standing wave formed as a result of reflection from a surface, the ratio of the amplitude at an antinode to that at node is x. The fraction of energy that is reflected is
  A)
   \[{{\left[ \frac{x-1}{x} \right]}^{2}}\] done clear
  B)
   \[{{\left[ \frac{x}{x+1} \right]}^{2}}\] done clear
  C)
  \[{{\left[ \frac{x-1}{x+1} \right]}^{2}}\] done clear
  D)
  \[{{\left[ \frac{1}{x} \right]}^{2}}\] done clear
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• question_answer54)
              String 1 is connected with string 2. The mass per unit length in string 1 is \[{{\mu }_{1}}\] and the mass per unit length in string 2 is 4\[{{\mu }_{1}}\]. The tension in the strings is T. A travelling wave is coming from the left. What fraction of the energy in the incident wave goes into string 2?
  A)
   1/8   done clear
  B)
   4/9     done clear
  C)
  2/3 done clear
  D)
  8/9 done clear
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• question_answer55)
  A uniform rope of length L and mass mi hangs vertically from a rigid support. A block of mass \[{{m}_{2}}\]is attached to the free end of the rope. A transverse pulse of wavelength \[{{\lambda }_{1}}\] is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is \[{{\lambda }_{2}}\] the ratio\[{{\lambda }_{2}}/{{\lambda }_{1}}\] is      
  A)
   \[\sqrt{\frac{{{m}_{1}}}{{{m}_{2}}}}\]           done clear
  B)
   \[\sqrt{\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{2}}}}\] done clear
  C)
  \[\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}\]            done clear
  D)
  \[\sqrt{\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{1}}}}\] done clear
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• question_answer56)
  A composite string is made up by joining two strings of different masses per unit length u, and 4u.The composite string is under the same tension. A transverse wave pulse 7= (6 mm) sin (5t + 40 x), where 't' is in seconds and 'x' is in metres, is sent along the lighter string towards the joint. The joint is at x = 0. The equation of the wave pulse reflected from the joint is
  A)
   \[Y=(2mm)\sin (5t-40x)\] done clear
  B)
   \[Y=(4mm)\sin (40x-5t)\] done clear
  C)
  \[Y=-(2mm)\sin (5t-40x)\] done clear
  D)
  \[Y=(2mm)\sin (5t-10x)\] done clear
  View Solution play_arrow

• question_answer57)
  A pipe of length \[{{\ell }_{1}}\], closed at one end is kept in a chamber of gas of density\[{{\rho }_{1}}\]. A second pipe open at both ends is placed in a second chamber of gas of density \[{{\rho }_{2}}\]. The compressibility of both the gases is equal Calculate the length of the second pipe if frequency of first overtone in both the cases is equal
  A)
   \[\frac{4}{3}{{\ell }_{1}}\sqrt{\frac{{{\rho }_{2}}}{{{\rho }_{1}}}}\] done clear
  B)
   \[\frac{4}{3}{{\ell }_{1}}\sqrt{\frac{{{\rho }_{1}}}{{{\rho }_{2}}}}\] done clear
  C)
  \[{{\ell }_{1}}\sqrt{\frac{{{\rho }_{2}}}{{{\rho }_{1}}}}\] done clear
  D)
  \[{{\ell }_{1}}\sqrt{\frac{{{\rho }_{1}}}{{{\rho }_{2}}}}\] done clear
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• question_answer58)
  Three sound waves of equal amplitudes have frequencies \[(v-1),\text{ }v,\text{ }(v+1).\] They superpose to give beats. The number of beats produced per second will be:
  A)
   3 done clear
  B)
   2      done clear
  C)
  1 done clear
  D)
  4 done clear
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• question_answer59)
  Two tones of frequencies \[{{n}_{1}}\]and \[{{n}_{2}}\]are sounded together. The beats can be heard distinctly when
  A)
   \[10<({{n}_{1}}-{{n}_{2}})<20\]        done clear
  B)
   \[5<({{n}_{1}}-{{n}_{2}})>20\] done clear
  C)
  \[5<({{n}_{1}}-{{n}_{2}})<20\] done clear
  D)
         \[0<({{n}_{1}}-{{n}_{2}})<10\] done clear
  View Solution play_arrow

• question_answer60)
  Two travelling waves \[{{y}_{1}}=A\sin [k(x-ct)]\] and\[{{y}_{2}}=A\sin [k(x+ct)]\]are superimposed on string. The distance between adjacent nodes is
  A)
   \[ct/\pi \]           done clear
  B)
   \[ct/2\pi \] done clear
  C)
  \[\pi /2k\]           done clear
  D)
  \[\pi /k\] done clear
  View Solution play_arrow

• question_answer61)
  Two factories are sounding their sirens at 800 Hz. A man goes from one factory to other at a speed of 2m/s. The velocity of sound is 320 m/s. The number of beats heard by the person in one second will be:
  A)
   2 done clear
  B)
   4      done clear
  C)
  8 done clear
  D)
  10 done clear
  View Solution play_arrow

• question_answer62)
  Two sound sources \[{{S}_{2}}\] and \[{{S}_{1}}\] emit pure     sinusoidal coherent waves in phase. If the   speed of sound is 340 m/s, then find out the     frequencies for which constructive interference   occurs at P.             
  A)
   170 Hz done clear
  B)
   340 Hz done clear
  C)
  510Hz done clear
  D)
  All of these done clear
  View Solution play_arrow

• question_answer63)
  A tuning fork arrangement (pair) produces 4 beats/sec with one fork of frequency 288 cps. A little wax is placed on the unknown fork and it then produces 2 beats/sec. The frequency of the unknown fork is
  A)
   286 cps done clear
  B)
   292 cps done clear
  C)
  294 cps done clear
  D)
  288 cps done clear
  View Solution play_arrow

• question_answer64)
  A tuning fork of frequency 512 Hz makes 4 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per sec when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
  A)
   \[510\,Hz\]           done clear
  B)
          \[514\,Hz\] done clear
  C)
  \[516\,Hz\]           done clear
  D)
         \[508\,Hz\] done clear
  View Solution play_arrow

• question_answer65)
  Two vibrating tuning forks produce progressive waves given by \[{{Y}_{1}}=4\sin 500\pi t\] and\[{{Y}_{2}}=2\sin 506\pi t\]. Number of beats produced per minute is
  A)
   360      done clear
  B)
   180   done clear
  C)
  60                     done clear
  D)
  3 done clear
  View Solution play_arrow

• question_answer66)
  The wavelength of two waves are 50 and 51 cm respectively. If the temperature of the room is \[20{}^\circ C\] then what will be the number of beats produced per second by these waves, when the speed of sound at \[0{}^\circ C\] is 332 m/s?
  A)
   24 done clear
  B)
   14 done clear
  C)
  10 done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer67)
  In the figure shown the wave speed is v. The velocity of car is \[{{v}_{0}}\]. The beat frequency for the observer will be         
  A)
   \[\frac{2{{f}_{0}}v{{v}_{0}}}{{{v}^{2}}+v_{0}^{2}}\] done clear
  B)
   \[\frac{2{{f}_{0}}{{v}^{2}}}{{{v}^{2}}-v_{0}^{2}}\] done clear
  C)
  \[\frac{2{{f}_{0}}v{{v}_{0}}}{{{v}^{2}}-{{v}_{0}}^{2}}\] done clear
  D)
  \[\frac{{{f}_{0}}v{{v}_{0}}}{{{v}^{2}}-{{v}_{0}}^{2}}\] done clear
  View Solution play_arrow

• question_answer68)
  An open pipe is in resonance in 2nd harmonic with frequency \[{{f}_{1}}\] Now one end of the tube is closed and frequency is increased to \[{{f}_{2}}\] such that the resonance again occurs in nth harmonic. Choose the correct option
  A)
   \[n=3,\,{{f}_{2}}=\frac{3}{4}{{f}_{1}}\] done clear
  B)
   \[n=3,\,{{f}_{2}}=\frac{5}{4}{{f}_{1}}\] done clear
  C)
  \[n=5,\,{{f}_{2}}=\frac{3}{4}{{f}_{1}}\] done clear
  D)
  \[n=5,\,{{f}_{2}}=\frac{5}{4}{{f}_{1}}\] done clear
  View Solution play_arrow

• question_answer69)
    Two sources of sound placed close to each other are emitting progressive waves given by\[{{y}_{1}}=4\sin 600\pi t\] and\[{{y}_{2}}=5\sin 608\pi t\]. An observer located near these two sources of sound will hear:
  A)
   4 beats per second with intensity ratio 25 : 16 between waxing and waning. done clear
  B)
   8 beats per second with intensity ratio 25 : 16 between waxing and waning done clear
  C)
  8 beats per second with intensity ratio 81: 1 between waxing and waning done clear
  D)
  4 beats per second with intensity ratio 81 : 1 between waxing and waning done clear
  View Solution play_arrow

• question_answer70)
  If wind blows from a stationary sounding object to a stationary listener, then the apparent frequency n? and actual frequency n are related as                      
  A)
   \[n'\ge n\] done clear
  B)
   \[n'<n\] done clear
  C)
  \[n'=n\] done clear
  D)
  \[n'>n\] done clear
  View Solution play_arrow

• question_answer71)
  A car is moving towards a high cliff. The car driver sounds a horn of frequency \[f\]. The reflected sound heard by the driver has as frequency \[2f\]. If v be the velocity of sound, then the velocity of the car, in the same velocity units, will be
  A)
   \[v/2\] done clear
  B)
   \[v/\sqrt{2}\] done clear
  C)
  \[v/3\]   done clear
  D)
  \[v/4\] done clear
  View Solution play_arrow

• question_answer72)

  Choose the false statement(s) from the following.

  I. Change in frequency due to Doppler effect will be positive if the distance between source and listener increases.

  II. Change in frequency due to Doppler effect will be negative if the distance between source and listener

  A)
   I only done clear
  B)
   II only done clear
  C)
  I and II done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer73)
  Two trains are moving towards each other with speeds of 20m/s and 15 m/s relative to the ground. The first train sounds a whistle of frequency 600 Hz. The frequency of the whistle heard by a passenger in the second train before the train meets, is (the speed of sound in air is 340 m/s)
  A)
   600 Hz done clear
  B)
   585 Hz done clear
  C)
  645 Hz done clear
  D)
  666 Hz done clear
  View Solution play_arrow

• question_answer74)
  Two trains move towards each other with the same speed. The speed of sound is 340 m/s. If the height of the tone of the whistle of one of them heard on the other changes 9/8 times, then the speed of each train should be
  A)
   20 m/s done clear
  B)
   2 m/s done clear
  C)
  200 m/s done clear
  D)
  2000 m/s done clear
  View Solution play_arrow

• question_answer75)
  A source producing sound of frequency 170 Hz is approaching a stationary observer with a velocity\[17m{{s}^{-1}}\]. The apparent change in the wavelength of sound heard by the observer is (speed of sound in air \[=340m{{s}^{-1}}\])
  A)
   0.1 m done clear
  B)
   0.2 m done clear
  C)
  0.4 m done clear
  D)
  0.5 m done clear
  View Solution play_arrow

• question_answer76)
  A man is watching two trains, one leaving and the other coming in with equal speeds of 4m/ sec. If they sound their whistles, each of frequency 240 Hz, the number of beats heard by the man (velocity of sound in air = 320 m/sec) will be equal to     
  A)
   6 done clear
  B)
   3      done clear
  C)
  0 done clear
  D)
  12 done clear
  View Solution play_arrow

• question_answer77)
  A sound source emits frequency of 180 Hz when moving towards a rigid wall with speed 5 m/s and an observer is moving away from wall with speed 5 m/s. Both source and observer moves on a straight line which is perpendicular to the wall. The number of beats per second heard by the observer will be [Speed of sound = 355 m/s]
  A)
   5 beats/s           done clear
  B)
   10 beats/s done clear
  C)
  6 beats/s            done clear
  D)
  8 beats/s done clear
  View Solution play_arrow

• question_answer78)
  A police car moving at 22 m/s, chases a motorcyclist. The policeman sounds his horn at 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz. The speed of the motorcycle, if it is given that he does not observe any beats is
  A)
   33 m/s done clear
  B)
   22 m/s done clear
  C)
  zero       done clear
  D)
  11 m/s done clear
  View Solution play_arrow

• question_answer79)
  In the figure shown a source of sound of frequency 510 Hz moves with constant velocity \[{{v}_{s}}=20m/s\] in the direction shown. The wind is blowing at a constant velocity \[{{v}_{w}}=20m/s\] towards an observer who is at rest at point B. Corresponding to the sound emitted by the source at initial position A, the frequency detected by the observer is equal to (speed of sound relative to air = 330 m/s)
  A)
   \[510\,Hz\]        done clear
  B)
   \[500\,Hz\] done clear
  C)
  \[525\,Hz\]         done clear
  D)
  \[550\,Hz\] done clear
  View Solution play_arrow

• question_answer80)
  A train has just completed a U-curve in a track which is a semicircle. The engine at the forward end of the semicircular part of the track while the last carriage is at the rear end of the semicircular track. The driver blows a whistle of frequency 200 Hz. Velocity of sound is 340 m/s. Then the apparent frequency as observed by a passenger in the middle of a train when the speed of the train is 30 m/s is     
  A)
   209 Hz done clear
  B)
   288 Hz done clear
  C)
  200 Hz done clear
  D)
  181 Hz done clear
  View Solution play_arrow

• question_answer81)
  A source of sound attached to the bob of a simple pendulum execute SHM. The difference between the apparent frequency of sound as received by an observer during its approach and recession at the mean position of the SHM motion is 2% of the natural frequency of the source. The velocity of the source at the mean position is (velocity of sound in the air is 340 m/s) [Assume velocity of sound source << velocity of sound in air]             
  A)
   1.4 m/s            done clear
  B)
          3.4 m/s done clear
  C)
  1.7 m/s           done clear
  D)
         2.1 m/s done clear
  View Solution play_arrow

• question_answer82)
  A source of sound S emitting waves of frequency 100 Hz and an observer 0 are located at some distance from each other. The source is moving with a speed of \[19.4m{{s}^{-1}}\] at an angle of \[60{}^\circ \] with the source observer line as shown in the figure. .The observer is at rest. The apparent frequency observed by the observer is (velocity of sound in air \[330m{{s}^{-1}}\])
  A)
   103 Hz          done clear
  B)
          106 Hz done clear
  C)
  97 Hz                done clear
  D)
  100 Hz done clear
  View Solution play_arrow

• question_answer83)
  A speeding motorcyclist sees trafic jam ahead of him. He slows down to 36 km/hour. He finds that traffic has eased and a car moving ahead of him at 18 km/hour is honking at a frequency of 1392 Hz. If the speeds of sound is 343 m/s, the frequency of the honk as heard by him will be :
  A)
   1332 Hz done clear
  B)
   1372 Hz done clear
  C)
  1412Hz done clear
  D)
  1464Hz done clear
  View Solution play_arrow

• question_answer84)
  An observer moves towards a stationary source of sound with a speed 1/8th of the speed of sound. The wavelength and frequency of the sound emitted are\[\lambda \]and\[f\]respectively. The apparent frequency and wavelength recorded by the observer are respectively.
  A)
   \[0.4f,0.4\lambda \] done clear
  B)
   \[0.6f,1.6\lambda \] done clear
  C)
  \[1.4f,\lambda \] done clear
  D)
  \[1.1f,\lambda \]   done clear
  View Solution play_arrow

• question_answer85)
  A parachutist jumps from the top of a very high tower with a siren of frequency 800 Hz on his back. Assume his initial velocity to be zero. After falling freely for 12s, he observes that the frequency of sound heard by him reflected from level ground below him is differing by 700Hz w.r.t. the original frequency. What was the height of tower. Velocity of sound in air is 330 m/s, and\[g=10m/{{s}^{2}}\].
  A)
   511.5 m. done clear
  B)
   1057.5 m. done clear
  C)
  757.5 m. done clear
  D)
  1215.5 m.             done clear
  View Solution play_arrow