# Solved papers for NEET Physics Wave Mechanics NEET PYQ-Wave Mechanics

### done NEET PYQ-Wave Mechanics Total Questions - 49

• question_answer1)  A transverse wave is represented by the equation $y={{y}_{0}}\sin \frac{2\pi }{\lambda }(vt-x)$ For what value of $\lambda$ is the maximum particle velocity equal to two times the wave velocity?    [AIPMT 1998]

A)
$\lambda =2\,\pi {{y}_{0}}$

B)
$\lambda =\frac{\pi {{v}_{0}}}{3}$

C)
$\lambda =\frac{\pi {{y}_{0}}}{2}$

D)
$\lambda =\pi {{y}_{0}}$

• question_answer2) A vehicle, with a horn of frequency n is moving with a velocity of 30 m/s in a direction perpendicular to the straight line joining the observer and the vehicle. The observer perceives the sound to have a frequency $n+{{n}_{1}}$. Then: (if the sound velocity in air is 300 m/s)                                           [AIPMT 1998]

A)
${{n}_{1}}=10\,n$

B)
${{n}_{1}}=0\,$

C)
${{n}_{1}}=0.1\,n$

D)
${{n}_{1}}=-\,0.1\,n$

• question_answer3) In a sinusoidal wave, the time required for a particular point, to move from maximum displacement to zero displacement is 0.170 s. The frequency of the wave is:                                                                         [AIPMT 1998]

A)
1.47 Hz

B)
0.36 Hz

C)
0.73 Hz

D)
2.94 Hz

• question_answer4) A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance $1.21\,\overset{o}{\mathop{A}}\,$ between them. The wavelength of the standing wave is:              [AIPMT 1998]

A)
$1.21\,\overset{o}{\mathop{A}}\,$

B)
$1.42\,\overset{o}{\mathop{A}}\,$

C)
$6.05\,\overset{o}{\mathop{A}}\,$

D)
$3.63\,\overset{o}{\mathop{A}}\,$

• question_answer5) Two waves of wavelength 50 cm and 51 cm produce 12 beats/s. The speed of sound is:                       [AIPMT 1999]

A)
306 m/s

B)
331 m/s

C)
340 m/s

D)
360 m/s

• question_answer6) A sonometer wire when vibrated in full length has frequency n. Now it is divided by the help of bridges into a number of segments of lengths${{l}_{1}},\,{{l}_{2}},\,{{l}_{3}}...$. When vibrated these segments have frequencies ${{n}_{1}},\,{{n}_{2}},\,{{n}_{3}},....$ then the correct relation is:                                           [AIPMT 2000]

A)
$n={{n}_{1}}+{{n}_{2}}+{{n}_{3}}+...$

B)
${{n}^{2}}=n_{1}^{2}+n_{2}^{2}+n_{3}^{2}+...$

C)
$\frac{1}{n}=\frac{1}{{{n}_{1}}}+\frac{1}{{{n}_{2}}}+\frac{1}{{{n}_{3}}}+...$

D)
$\frac{1}{\sqrt{n}}=\frac{1}{\sqrt{{{n}_{1}}}}+\frac{1}{\sqrt{{{n}_{2}}}}+\frac{1}{\sqrt{{{n}_{3}}}}+...$

• question_answer7) Two strings A and B have lengths ${{l}_{A}}$ and ${{l}_{B}}$ and carry masses ${{M}_{A}}$ and ${{M}_{B}}$ at their lower ends, the upper ends being supported by rigid supports. If ${{n}_{A}}$ and ${{n}_{B}}$ are their frequencies of their vibrations and ${{n}_{A}}=2{{n}_{B}},$ then:                                                                  [AIPMT 2000]

A)
${{l}_{A}}=4{{l}_{B}},$ regardless of masses

B)
${{l}_{B}}=4{{l}_{A}},$ regardless of masses

C)
${{M}_{A}}=2{{M}_{B}},\,{{l}_{A}}=2{{l}_{B}}$

D)
${{M}_{B}}=2{{M}_{A}},\,{{l}_{B}}=2{{l}_{A}}$

• question_answer8)                                                             Equations of two progressive waves are given by ${{y}_{1}}=a\sin \,(\omega t-{{\phi }_{1}})$ and ${{y}_{2}}=a\sin \,(\omega t-{{\phi }_{2}})$. If amplitude and time period of resultant wave are same as that of both the waves, then $({{\phi }_{1}}-{{\phi }_{2}})\,$ is:                                                                               [AIPMT 2001]

A)
$\frac{\pi }{3}$

B)
$\frac{2\pi }{3}$

C)
$\frac{\pi }{6}$

D)
$\frac{\pi }{4}$

• question_answer9) The equation of a wave is given by:                      [AIPMT 2001] $y=a\sin \left( 100t-\frac{x}{10} \right),$ where x and y are in metre and t in second; then velocity of wave is:

A)
0.1 m/s

B)
10 m/s

C)
100 m/s

D)
1000 m/s

• question_answer10) The frequency of a vibrating wire is $n$. If tension is doubled, density is halved and diameter is doubled, then new frequency will be:                                                                                                              [AIPMT 2001]

A)
n

B)
$\frac{n}{\sqrt{2}}$

C)
2n

D)
4n

• question_answer11) A wave of amplitude A = 0.2 m, velocity v = 360 m/s and wavelength 60 m is travelling along positive x-axis, then the correct expression for the wave is :                                                                                      [AIPMT 2002]

A)
$y=0.2\sin \,2\pi \,\left( 6\,t+\frac{x}{60} \right)$

B)
$y=0.2\sin \,\pi \,\left( 6\,t+\frac{x}{60} \right)$

C)
$y=0.2\sin \,2\pi \,\left( 6\,t-\frac{x}{60} \right)$

D)
$y=0.2\sin \,\,\pi \,\left( 6\,t-\frac{x}{60} \right)$

• question_answer12) A whistle revolves in a circle with angular velocity $\omega =20$ rad/s using a string of length 50 cm. If the actual frequency of sound from the whistle is 385 Hz, then the minimum frequency heard by the observer far away from the centre is : (velocity of sound $v=340\text{ }m/s$)                                                                             [AIPMT 2002]

A)
385 Hz

B)
374 Hz

C)
394 Hz

D)
333 Hz

• question_answer13) An observer moves towards a stationary source of sound with a speed 1/5th of the speed of sound. The wavelength and frequency of the source emitted are $\lambda$ and f respectively. The apparent frequency and wavelength recorded by the observer are respectively:           [AIPMT 2003]

A)
$f,\,\,1,\,\,2\,\lambda$

B)
$0.8f,\,\,0.8\lambda$

C)
$1.2\,f,\,\,1.2\,\lambda$

D)
$1.2\,f,\,\lambda$

• question_answer14) 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 a frequency $2f$. If$v$ be the velocity of sound, then the velocity of the car, in the same velocity units, will be:                                                                                                                                                      [AIPMT (S) 2004]

A)
$\frac{v}{\sqrt{2}}$

B)
$\frac{v}{3}$

C)
$\frac{v}{4}$

D)
$\frac{v}{2}$

• question_answer15)  The phase difference between two waves, represented by                      [AIPMT (S) 2004] ${{y}_{1}}={{10}^{-6}}\sin [100t+(x/50)+0.5]\,m$ ${{y}_{2}}={{10}^{-6}}\cos [100t+(x/50)]\,m$ where x is expressed in metres and t is expressed in seconds, is approximately:

A)

B)

C)

D)

• question_answer16) A point source emits sound equally in all directions in a non-absorbing medium. Two points P and Q are at distance of 2 m and 3 m respectively from the source. The ratio of the intensities of the waves at P and Q is:                      [AIPMT (S) 2005]

A)
9 : 4

B)
2 : 3

C)
3 : 2

D)
4 : 9

• question_answer17) 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:                            [AIPMT (S) 2005]

A)
360

B)
180

C)
3

D)
60

• question_answer18) Two sound waves with wavelengths 5.0 m and 5.5 m respectively, each propagate in a gas with velocity 330 m/s. We expect the following number of beats per second:                                                          [AIPMT (S) 2006]

A)
12

B)
0

C)
1

D)
6

• question_answer19)  A transverse wave propagating along x-axis is represented by:                           [AIPMT (S) 2006] $y\,(x,t)=8.0\,\sin \,\left( 0.5\,\pi x-4\pi t-\frac{\pi }{4} \right)$ where x is in metres and t is in seconds. The speed of the wave is:

A)
$4\,\pi \,m/s$

B)
$0.5\,\pi \,m/s$

C)
$\frac{\pi }{4}\,m/s$

D)
$8\,\,m/s$

• question_answer20) The time of reverberation of a room A is one second. What will be the time (in seconds) of reverberation of a room, having all the dimensions double of those of room A?                                                 [AIPMT (S) 2006]

A)
2

B)
4

C)
$\frac{1}{2}$

D)
1

• question_answer21) Which one of the following statements is true?                                                         [AIPMT (S) 2006]

A)
Both light and sound waves in air are transverse

B)
The sound waves in air are longitudinal while the light waves are transverse

C)
Both light and sound waves in air are longitudinal

D)
Both light and sound waves can travel in vacuum

• question_answer22) Two periodic waves of intensities ${{I}_{1}}$ and ${{I}_{2}}$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is                                              [AIPMPT (S) 2008]

A)
${{I}_{1}}+{{I}_{2}}$

B)
${{(\sqrt{{{I}_{1}}}+\sqrt{{{I}_{2}}})}^{2}}$

C)
${{(\sqrt{{{I}_{1}}}-\sqrt{{{I}_{2}}})}^{2}}$

D)
$2({{I}_{1}}+{{I}_{2}})$

• question_answer23) The wave described by $y=0.25\sin (10\pi x-2\pi t),$ where x and y are in metre and t in second, is a wave travelling along the                                                                                                             [AIPMPT (S) 2008]

A)
- ve x direction with frequency 1 Hz

B)
+ve x direction with frequency $\pi$ Hz and wavelength $\lambda =0.2m$

C)
+ve x direction with frequency 1 Hz and wavelength $\lambda =0.2m$

D)
- ve x direction with amplitude 0.25 m and wavelength $\lambda =0.2m$

• question_answer24)  A wave in a string has an amplitude of 2 cm. The wave travels in the +ve direction of x axis with a speed of $128\,m{{s}^{-1}}$ and it is noted that 5 complete waves fit in 4 m length of the string. The equation describing the wave is                                                                       [AIPMT (S) 2009]

A)
$y=(0.02)\,m\,\sin \,(7.85x+1005\,t)$

B)
$y=(0.02)\,m\,\sin \,(15.7x-2010\,t)$

C)
$y=(0.02)\,m\,\sin \,(15.7x+2010\,t)$

D)
$y=(0.02)\,m\,\sin \,(7.85x-1005\,t)$

• question_answer25) The driver of a car travelling with speed $30\,m{{s}^{-2}}$ towards a hill sounds a horn of frequency 600 Hz. If the velocity of sound in air is $330\,m{{s}^{-1}},$ tile-frequency of reflected sound as heard by driver is [AIPMT (S) 2009]

A)
550 Hz

B)
555.5 Hz

C)
720 Hz

D)
500 Hz

• question_answer26) Each of the two strings of length 51.6 cm and 49.1 cm are tensioned separately by 20 N force. Mass per unit length of both the strings is same and equal to $1\,g{{m}^{-1}}$. When both the strings vibrate simultaneously the number of beats is [AIPMT (S) 2009]

A)
5

B)
7

C)
8

D)
3

• question_answer27) A tuning fork of frequency 512 Hz makes 4 beats/s with the vibrating string of a piano. The beat frequency decreases to 2 beats/s when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was                                                                                                                    [AIPMT (S) 2010]

A)
510 Hz

B)
514 Hz

C)
516 Hz

D)
508 Hz

• question_answer28) Sound waves travel at 350 m/s through a warn air and at 3500 m/s  through brass. The wavelength of a 700 Hz acoustic wave as it enters brass from warm air                                                                             [AIPMT (S) 2011]

A)
increases by a factor 20

B)
increases by a factor 10

C)
decreases by a factor 20

D)
decreases by a factor 10

• question_answer29) The equation of a simple harmonic wave is given by$y=3\sin \frac{\pi }{2}(50t-x),$ where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is                                 [AIPMT (M) 2012]

A)
$2\pi$

B)
$\frac{3}{2}\pi$

C)
$3\pi$

D)
$\frac{2}{3}\pi$

• question_answer30) A train moving at a speed of $220\,m{{s}^{-1}}$ towards a stationary object, emits a sound of frequency 1000 Hz. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the driver of the train is (speed of sound in air is$330m{{s}^{-1}}$)                                                          [AIPMT (M) 2012]

A)
3500 Hz

B)
4000 Hz

C)
5000 Hz

D)
3000 Hz

• question_answer31) When a string is divided into three segments of lengths ${{l}_{1}},{{l}_{2}}$  and ${{l}_{3}},$ the fundamental frequencies of these three segments are ${{v}_{1}},{{v}_{2}}$ and ${{v}_{3}}$ respectively. The   original fundamental frequency (v) of the string is                                                                             [AIPMT (S) 2012]

A)
$\sqrt{v}=\sqrt{{{v}_{1}}}+\sqrt{{{v}_{2}}}+\sqrt{{{v}_{3}}}$

B)
$v={{v}_{1}}+{{v}_{2}}+{{v}_{3}}$

C)
$\frac{1}{v}=\frac{1}{{{v}_{1}}}+\frac{1}{{{v}_{2}}}+\frac{1}{{{v}_{3}}}$

D)
$\frac{1}{\sqrt{v}}=\frac{1}{\sqrt{{{v}_{1}}}}+\frac{1}{\sqrt{{{v}_{2}}}}+\frac{1}{\sqrt{{{v}_{3}}}}$

• question_answer32) A wave travelling in the positive a-direction having displacement along .y-direction as 1 m, wavelength $2\pi m$ and frequency of $\frac{1}{\pi }\,Hz$ is represented by                                       [NEET 2013]

A)
$y=\sin (x-2t)$

B)
$y=\sin (2\pi x-2\pi t)$

C)
$y=\sin (10\pi x-20\pi t)$

D)
$y=\sin (2\pi x+2\pi t)$

• question_answer33) If we study the vibration of a pipe open at both ends, then the following statements is not true              [NEET 2013]

A)
Open end will be anti-node

B)
Odd harmonics of the fundamental frequency will be generated

C)
All harmonics of the fundamental frequency will be generated

D)
Pressure change will be maximum at both ends

• question_answer34) A source of unknown frequency gives 4 beats/s when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency 513 Hz. The unknown frequency is                                                                                               [NEET 2013]

A)
254 Hz

B)
246 Hz

C)
240 Hz

D)
260 Hz

• question_answer35) 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                             [NEET 2014]

A)
$\frac{1}{n}=\frac{1}{{{n}_{1}}}+\frac{1}{{{n}_{2}}}+\frac{1}{{{n}_{3}}}$

B)
$\frac{1}{\sqrt{n}}=\frac{1}{\sqrt{{{n}_{1}}}}+\frac{1}{\sqrt{{{n}_{2}}}}+\frac{1}{\sqrt{{{n}_{3}}}}$

C)
$\sqrt{n}=\sqrt{{{n}_{1}}}+\sqrt{{{n}_{2}}}+\sqrt{{{n}_{3}}}$

D)
$n={{n}_{1}}+{{n}_{2}}+{{n}_{3}}$

• question_answer36) The number of possible natural oscillations of air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are (velocity of sound$=340\,m{{s}^{-1}}$)     [NEET 2014]

A)
4

B)
5

C)
7

D)
6

• question_answer37) A speeding motorcyclist sees traffic jam ahead of him. He slows down to 36 km/h. He finds that traffic has eased and a car moving head of him at 18 km/h is honking at a frequency of 1392 Hz. If the speed of sound is 343 m/s, the frequency of the honk as heard by him will be                                                                                                         [NEET 2014]

A)
1332 Hz

B)
1372 Hz

C)
1412 Hz

D)
1454 Hz

• question_answer38) 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                                       [NEET  2015]

A)
80 cm

B)
100 cm

C)
120 cm

D)
140 cm

• question_answer39)  A source +e of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of $19.4\,m{{s}^{-1}}$ at an angle of ${{60}^{o}}$ with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air $330\,m{{s}^{-1}}$), is                                                                                                  [NEET (Re) 2015]

A)
100 Hz

B)
103 Hz

C)
106 Hz

D)
97 Hz

• question_answer40) 4.0 g of a gas occupies 22.4 L at NTP. The specific heat capacity of the gas at constant volume is $5.0J{{K}^{-1}}mo{{l}^{-1}}$. If the speed of sound in this gas at NTP is $952\,m{{s}^{-1}}$ then the heat capacity at constant pressure is (Take gas constant$R=8.3\,J{{K}^{-1}}mo{{l}^{-1}}$)      [NEET (Re) 2015]

A)
$8.0\,J{{K}^{-1}}mo{{l}^{-1}}$

B)
$7.5\,\,J{{K}^{-1}}mo{{l}^{-1}}$

C)
$7.0\,\,J{{K}^{-1}}mo{{l}^{-1}}$

D)
$8.5\,\,J{{K}^{-1}}mo{{l}^{-1}}$

• question_answer41) 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. The lowest resonant frequency for this strings is                                                                                                                                          [NEET (Re) 2015]

A)
155 Hz

B)
205 Hz

C)
10.5 Hz

D)
105 Hz

• question_answer42) A siren emitting a sound of frequency 800 Hz moves away from an observer towards a cliff at a speed of $15\,m{{s}^{-1}}$. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is :      [NEET - 2016] (Take velocity of sound in air $=330\,m{{s}^{-1}}$)

A)
765 Hz

B)
800 Hz

C)
838 Hz

D)
885 Hz

• question_answer43) A uniform rope of length L and mass ${{m}_{1}}$ 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 :                                                                       [NEET - 2016]

A)
$\sqrt{\frac{{{m}_{1}}}{{{m}_{2}}}}$

B)
$\sqrt{\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{2}}}}$

C)
$\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}$

D)
$\sqrt{\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{1}}}}$

• question_answer44) An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is:               [NEET - 2016]

A)
66.7 cm

B)
100 cm

C)
150 cm

D)
200 cm

• question_answer45) The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system?                                      [NEET-2017]

A)
40 Hz

B)
10 Hz

C)
20 Hz

D)
30 Hz

• question_answer46) Two cars moving in opposite directions approach each other with speed of 22 m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is [velocity of sound 340 m/s]

A)
448 Hz

B)
350 Hz

C)
361 Hz

D)
411 Hz

• question_answer47) The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is                                          [NEET - 2018]

A)
12.5 cm

B)
8 cm

C)
13.2 cm

D)
16 cm

• question_answer48)  A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of $\text{27 }\!\!{}^\text{o}\!\!\text{ C}$ two successive resonances are produced at 20 cm and 73 cm of column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at $\text{27 }\!\!{}^\text{o}\!\!\text{ C}$ is                                                                                      [NEET - 2018]

A)
350 m/s

B)
339 m/s

C)
330 m/s

D)
300 m/s

• question_answer49) In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6 Hz. When tension in B is slightly decreased, the beat frequency increases to 7 Hz. If the frequency of A is 530 Hz, the original frequency of B will be:                                                                                               [NEET 2020]

A)
524 Hz

B)
536 Hz

C)
537 Hz

D)
523 Hz