JEE Main & Advanced Physics Wave Mechanics Question Bank

done Vibration of String Total Questions - 52

• question_answer1)
  A string fixed at both the ends is vibrating in two segments. The wavelength of the corresponding wave is [SCRA 1994]
  A)
             \[\frac{l}{4}\]                        done clear
  B)
                    \[\frac{l}{2}\] done clear
  C)
             l       done clear
  D)
             2l done clear
  View Solution play_arrow

• question_answer2)
  A 1 cm long string vibrates with fundamental frequency of 256 Hz. If the length is reduced to \[\frac{1}{4}cm\] keeping the tension unaltered, the new fundamental frequency will be [BHU 1997]
  A)
             64   done clear
  B)
             256 done clear
  C)
             512 done clear
  D)
             1024 done clear
  View Solution play_arrow

• question_answer3)
  Standing waves are produced in a 10 m long stretched string. If the string vibrates in 5 segments and the wave velocity is 20 m/s, the frequency is [CBSE PMT 1997; AIIMS 1998; JIPMER 2000]
  A)
             2 Hz                                           done clear
  B)
             4 Hz done clear
  C)
             5 Hz                                           done clear
  D)
             10 Hz done clear
  View Solution play_arrow

• question_answer4)
  The velocity of waves in a string fixed at both ends is 2 m/s. The string forms standing waves with nodes 5.0 cm apart. The frequency of vibration of the string in Hz is [SCRA 1998]
  A)
             40   done clear
  B)
             30 done clear
  C)
             20   done clear
  D)
             10 done clear
  View Solution play_arrow

• question_answer5)
  Which of the following is the example of transverse wave  [CPMT 1999]
  A)
             Sound waves done clear
  B)
             Compressional waves in a spring done clear
  C)
             Vibration of string               done clear
  D)
             All of these done clear
  View Solution play_arrow

• question_answer6)
  A stretched string of 1m length and mass \[5\times {{10}^{-4}}kg\] is having tension of 20N. If it is plucked at 25cm from one end then it will vibrate with frequency [RPET 1999; RPMT 2002]
  A)
             100 Hz                                      done clear
  B)
             200 Hz done clear
  C)
             256 Hz                                      done clear
  D)
             400 Hz done clear
  View Solution play_arrow

• question_answer7)
  Two similar sonometer wires given fundamental frequencies of 500Hz. These have same tensions. By what amount the tension be increased in one wire so that the two wires produce 5 beats/sec                [RPET 1999]
  A)
             1%  done clear
  B)
             2% done clear
  C)
             3%  done clear
  D)
             4% done clear
  View Solution play_arrow

• question_answer8)
  A string is producing transverse vibration whose equation is \[y=0.021\ \sin (x+30t)\], Where x and y are in meters and \[t\] is in seconds. If the linear density of the string is \[1.3\times {{10}^{-4}}\]kg/m, then the tension in the string in \[N\] will be [RPET 1999; RPMT 2002]
  A)
             10   done clear
  B)
             0.5 done clear
  C)
             1     done clear
  D)
             0.117 done clear
  View Solution play_arrow

• question_answer9)
  If the tension of sonometer?s wire increases four times then the fundamental frequency of the wire will increase by [RPMT 1999]
  A)
             2 times                                    done clear
  B)
             4 times done clear
  C)
             1/2 times                                done clear
  D)
             None of the above done clear
  View Solution play_arrow

• question_answer10)
  If vibrations of a string are to be increased by a factor of two, then tension in the string must be made [AIIMS 1999; Pb. PET 2000]
  A)
             Half                                           done clear
  B)
             Twice done clear
  C)
             Four times                             done clear
  D)
             Eight times done clear
  View Solution play_arrow

• question_answer11)
  Four wires of identical length, diameters and of the same material are stretched on a sonometre wire. If the ratio of their tensions is 1 : 4 : 9 : 16 then the ratio of their fundamental frequencies are                [KCET 2000]
  A)
             16 : 9 : 4 : 1                             done clear
  B)
             4 : 3 : 2 : 1 done clear
  C)
             1 : 4 : 2 : 16                             done clear
  D)
             1 : 2 : 3 : 4 done clear
  View Solution play_arrow

• question_answer12)
  A tuning fork vibrating with a sonometer having 20 cm wire produces 5 beats per second. The beat frequency does not change if the length of the wire is changed to 21 cm. the frequency of the tuning fork (in Hertz) must be [UPSEAT 2000; Pb. PET 2004]
  A)
             200 done clear
  B)
             210 done clear
  C)
             205 done clear
  D)
             215 done clear
  View Solution play_arrow

• question_answer13)
  A stretched string of length \[l,\] fixed at both ends can sustain stationary waves of wavelength \[\lambda ,\] given by [UPSEAT 2000; Pb. PET 2004; CPMT 2005]
  A)
             \[\lambda =\frac{{{n}^{2}}}{2l}\]                                     done clear
  B)
             \[\lambda =\frac{{{l}^{2}}}{2n}\] done clear
  C)
             \[\lambda =\frac{2l}{n}\] done clear
  D)
             \[\lambda =2l\ n\] done clear
  View Solution play_arrow

• question_answer14)
  If you set up the seventh harmonic on a string fixed at both ends, how many nodes and antinodes are set up in it [AMU 2000]
  A)
             8, 7 done clear
  B)
             7, 7 done clear
  C)
             8, 9 done clear
  D)
             9, 8 done clear
  View Solution play_arrow

• question_answer15)
  If you set up the ninth harmonic on a string fixed at both ends, its frequency compared to the seventh harmonic [AMU (Engg.) 2000]
  A)
             Higher                                      done clear
  B)
             Lower done clear
  C)
             Equal                                        done clear
  D)
             None of the above done clear
  View Solution play_arrow

• question_answer16)
  Frequency of a sonometer wire is n. Now its tension is increased 4 times and its length is doubled then new frequency will be                                                         [RPET 2000]
  A)
             n/2 done clear
  B)
             4n done clear
  C)
             2n   done clear
  D)
             n done clear
  View Solution play_arrow

• question_answer17)
  A device used for investigating the vibration of a fixed string or wire is                                   [BHU 2000]
  A)
             Sonometer                            done clear
  B)
             barometer done clear
  C)
             Hydrometer                          done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer18)
  A string on a musical instrument is 50 cm long and its fundamental frequency is 270 Hz. If the desired frequency of 1000 Hz is to be produced, the required length of the string is  [EAMCET (Engg.) 1998; CPMT 2000; Pb. PET 2001]
  A)
             13.5 cm                                    done clear
  B)
             2.7 cm done clear
  C)
             5.4 cm                                      done clear
  D)
             10.3 cm done clear
  View Solution play_arrow

• question_answer19)
  The tension in a piano wire is 10N. What should be the tension in the wire to produce a note of double the frequency                                                                       [AIIMS 2001]
  A)
             5 N done clear
  B)
             20 N done clear
  C)
             40 N                                          done clear
  D)
             80 N done clear
  View Solution play_arrow

• question_answer20)
  To increase the frequency from 100 Hz to 400 Hz the tension in the string has to be changed by [RPET 2001]
  A)
             4 times                                    done clear
  B)
             16 times done clear
  C)
             20 times                                  done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer21)
  In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to \[\frac{3}{4}\]th of the original length and the tension is changed. The factor by which the tension is to be changed, is                    [EAMCET 2001]
  A)
             \[\frac{3}{8}\]                       done clear
  B)
             \[\frac{2}{3}\] done clear
  C)
             \[\frac{8}{9}\]                       done clear
  D)
             \[\frac{9}{4}\] done clear
  View Solution play_arrow

• question_answer22)
  A string of 7 m length has a mass of 0.035 kg. If tension in the string is 60.5 N, then speed of a wave on the string is [CBSE PMT 2001]
  A)
             77 m/s                                     done clear
  B)
             102 m/s done clear
  C)
             110 m/s                                   done clear
  D)
             165 m/s done clear
  View Solution play_arrow

• question_answer23)
  A second harmonic has to be generated in a string of length \[l\] stretched between two rigid supports. The point where the string has to be plucked and touched are  [KCET 2001]
  A)
             Plucked at \[\frac{l}{4}\] and touch at \[\frac{l}{2}\] done clear
  B)
             Plucked at \[\frac{l}{4}\] and touch at \[\frac{3l}{4}\] done clear
  C)
             Plucked at \[\frac{l}{2}\] and touched at \[\frac{l}{4}\] done clear
  D)
             Plucked at \[\frac{l}{2}\] and touched at \[\frac{3l}{4}\] done clear
  View Solution play_arrow

• question_answer24)
  Transverse waves of same frequency are generated in two steel wires A and B. The diameter of A is twice of B and the tension in A is half that in B. The ratio of velocities of wave in A and B is                                          [KCET 2001]
  A)
             \[1\ :\ 3\sqrt{2}\]                done clear
  B)
             \[1\ :\ 2\sqrt{2}\] done clear
  C)
             \[1\ :\ 2\]                                done clear
  D)
             \[\sqrt{2}\ :\ 1\] done clear
  View Solution play_arrow

• question_answer25)
  A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of 9 kg is suspended from the wire. When this mass is replaced by a mass M, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of M is  [IIT-JEE (Screening) 2002]
  A)
             25 kg                                        done clear
  B)
             5 kg done clear
  C)
             12.5 kg                                     done clear
  D)
             1/25 kg done clear
  View Solution play_arrow

• question_answer26)
  The tension of a stretched string is increased by 69%. In order to keep its frequency of vibration constant, its length must be increased by                                                    [KCET 2002]
  A)
             20%                                           done clear
  B)
             30% done clear
  C)
             \[\sqrt{69}%\]                      done clear
  D)
             69% done clear
  View Solution play_arrow

• question_answer27)
  The length of a sonometer wire tuned to a frequency of 250 Hz is 0.60 metre. The frequency of tuning fork with which the vibrating wire will be in tune when the length is made 0.40 metre is                                 [JIPMER 2002]
  A)
             250 Hz                                      done clear
  B)
             375 Hz done clear
  C)
             256 Hz                                      done clear
  D)
             384 Hz done clear
  View Solution play_arrow

• question_answer28)
  Length of a string tied to two rigid supports is 40 cm. Maximum length (wavelength in cm) of a stationary wave produced on it is                                                            [AIEEE 2002]
  A)
             20   done clear
  B)
             80 done clear
  C)
             40   done clear
  D)
             120 done clear
  View Solution play_arrow

• question_answer29)
  A string in musical instrument is 50 cm long and its fundamental frequency is 800 Hz. If a frequency of 1000 Hz is to be produced, then required length of string is  [AIIMS 2002]
  A)
             62.5 cm                                    done clear
  B)
             50 cm done clear
  C)
             40 cm                                       done clear
  D)
             37.5 cm done clear
  View Solution play_arrow

• question_answer30)
  Two wires are in unison. If the tension in one of the wires is increased by 2%, 5 beats are produced per second. The initial frequency of each wire is                            [MP PET 2002]
  A)
             200 Hz                                      done clear
  B)
             400 Hz done clear
  C)
             500 Hz                                      done clear
  D)
             1000 Hz done clear
  View Solution play_arrow

• question_answer31)
  Two uniform strings A and B made of steel are made to vibrate under the same tension. if the first overtone of A is equal to the second overtone of B and if the radius of A is twice that of B, the ratio of the lengths of the strings is [EAMCET 2003]
  A)
              1: 2                                           done clear
  B)
             1 : 3 done clear
  C)
             1 : 4                                           done clear
  D)
             1 : 6 done clear
  View Solution play_arrow

• question_answer32)
  If the length of a stretched string is shortened by 40% and the tension is increased by 44%, then the ratio of the final and initial fundamental frequencies is [EAMCET 2003]
  A)
             2 : 1                                           done clear
  B)
             3 : 2 done clear
  C)
             3 : 4                                           done clear
  D)
             1 : 3 done clear
  View Solution play_arrow

• question_answer33)
  Two wires are fixed in a sonometer. Their tensions are in the ratio 8 : 1. The lengths are in the ratio \[36:35.\] The diameters are in the ratio 4 : 1. Densities of the materials are in the ratio 1 : 2. If the lower frequency in the setting is 360 Hz. the beat frequency when the two wires are sounded together is                                              [KCET 2003]
  A)
             5     done clear
  B)
             8 done clear
  C)
             6     done clear
  D)
             10 done clear
  View Solution play_arrow

• question_answer34)
  The first overtone of a stretched wire of given length is 320 Hz. The first harmonic is :                     [DPMT 2004]
  A)
             320 Hz                                      done clear
  B)
             160 Hz done clear
  C)
             480 Hz                                      done clear
  D)
             640 Hz done clear
  View Solution play_arrow

• question_answer35)
  Two perfectly identical wires are in unison. When the tension in one wire is increased by 1%, then on sounding them together 3 beats are heard in 2 sec. The initial frequency of each wire is :                                              [Pb. PET 2002]
  A)
             \[220{{s}^{-1}}\]                  done clear
  B)
             \[320{{s}^{-1}}\] done clear
  C)
             \[150{{s}^{-1}}\]                  done clear
  D)
             \[300{{s}^{-1}}\] done clear
  View Solution play_arrow

• question_answer36)
  A tuning fork of frequency 392 Hz, resonates with 50 cm length of a string under tension (T). If length of the string is decreased by 2%, keeping the tension constant, the number of beats heard when the string and the tuning fork made to vibrate simultaneously is                                        [BHU 2004]
  A)
             4     done clear
  B)
             6 done clear
  C)
             8     done clear
  D)
             12 done clear
  View Solution play_arrow

• question_answer37)
  The sound carried by air from a sitar to a listener is a wave of the following type                                [MP PMT 1987; RPET 2001]
  A)
             Longitudinal stationary     done clear
  B)
             Transverse progressive done clear
  C)
             Transverse stationary       done clear
  D)
             Longitudinal progressive done clear
  View Solution play_arrow

• question_answer38)
  In Melde?s experiment in the transverse mode, the frequency of the tuning fork and the frequency of the waves in the strings are in the ratio                                           [KCET 2004]                                                            
  A)
             1 : 1                                           done clear
  B)
             1 : 2 done clear
  C)
             2 : 1                                           done clear
  D)
             4 : 1 done clear
  View Solution play_arrow

• question_answer39)
  The frequency of transverse vibrations in a stretched string is 200 Hz. If the tension is increased four times and the length is reduced to one-fourth the original value, the frequency of vibration will be                       [EAMCET (Med.) 1999]
  A)
             25 Hz                                        done clear
  B)
             200 Hz done clear
  C)
             400 Hz                                      done clear
  D)
             1600 Hz done clear
  View Solution play_arrow

• question_answer40)
  Three similar wires of frequency n1, n2 and n3 are joined to make one wire. Its frequency will be                                                                                        [CBSE PMT 2000]
  A)
                                                       \[n={{n}_{1}}+{{n}_{2}}+{{n}_{3}}\]                                done clear
  B)
             \[\frac{1}{n}=\frac{1}{{{n}_{1}}}+\frac{1}{{{n}_{2}}}+\frac{1}{{{n}_{3}}}\] done clear
  C)
             \[\frac{1}{\sqrt{n}}=\frac{1}{\sqrt{{{n}_{1}}}}+\frac{1}{\sqrt{{{n}_{2}}}}+\frac{1}{\sqrt{{{n}_{3}}}}\]              done clear
  D)
             \[\frac{1}{{{n}^{1}}}=\frac{1}{n_{1}^{2}}+\frac{1}{n_{2}^{2}}+\frac{1}{n_{3}^{2}}\] done clear
  View Solution play_arrow

• question_answer41)
  A steel rod 100 cm long is clamped at its mid-point. The funda-mental frequency of longitudinal vibrations of the rod is given to be 2.53 kHz. What is the speed of sound in steel           [AFMC 2000]
  A)
             5.06 km/s                               done clear
  B)
             6.06 km/s done clear
  C)
             7.06 km/s                               done clear
  D)
             8.06 km/s done clear
  View Solution play_arrow

• question_answer42)
  Two wires are producing fundamental notes of the same frequency. Change in which of the following factors of one wire will not produce beats between them  [BHU (Med.) 1999]
  A)
             Amplitude of the vibrations done clear
  B)
             Material of the wire done clear
  C)
             Stretching force done clear
  D)
             Diameter of the wires done clear
  View Solution play_arrow

• question_answer43)
  Calculate the frequency of the second harmonic formed on a string of length 0.5 m and mass 2 ´ 10?4 kg when stretched with a tension of 20 N                                        [BHU (Med.) 2000]
  A)
             274.4 Hz                                  done clear
  B)
             744.2 Hz done clear
  C)
             44.72 Hz                                  done clear
  D)
             447.2 Hz done clear
  View Solution play_arrow

• question_answer44)
  The fundamental frequency of a string stretched with a weight of 4 kg is 256 Hz. The weight required to produce its octave is                                                    [J & K CET 2000]
  A)
             4 kg wt                                    done clear
  B)
             8 kg wt done clear
  C)
             12 kg wt                                  done clear
  D)
             16 kg wt   done clear
  View Solution play_arrow

• question_answer45)
  Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n1 and the other with frequency n2. The ratio n1/n2 is given by [IIT-JEE (Screening) 2000]
  A)
             2     done clear
  B)
             4  done clear
  C)
             8     done clear
  D)
             1 done clear
  View Solution play_arrow

• question_answer46)
  If the tension and diameter of a sonometer wire of fundamental frequency n are doubled and density is halved then its fundamental frequency will become [CBSE PMT 2001]
  A)
             \[\frac{n}{4}\]                      done clear
  B)
             \[\sqrt{2}\,n\] done clear
  C)
             n     done clear
  D)
             \[\frac{n}{\sqrt{2}}\] done clear
  View Solution play_arrow

• question_answer47)
  In a sonometer wire, the tension is maintained by suspending a 50.7 kg mass from the free end of the wire. The suspended mass has a volume of 0.0075 m3. The fundamental frequency of the wire is 260 Hz. If the suspended mass is completely submerged in water, the fundamental frequency will become (take g = 10 ms?2)  [KCET 2001]
  A)
             240 Hz                                      done clear
  B)
             230 Hz done clear
  C)
             220 Hz                                      done clear
  D)
             200 Hz done clear
  View Solution play_arrow

• question_answer48)
  A string is rigidly tied at two ends and its equation of vibration is given by \[y=\cos 2\pi \,t\sin \sin \pi x.\] Then minimum length of string is                                                           [RPMT 2001]
  A)
             1 m                                            done clear
  B)
             \[\frac{1}{2}m\] done clear
  C)
             5 m                                            done clear
  D)
             2pm done clear
  View Solution play_arrow

• question_answer49)
  Fundamental frequency of sonometer wire is n. If the length, tension and diameter of wire are tripled, the new fundamental frequency is                                         [DPMT 2002]
  A)
             \[\frac{n}{\sqrt{3}}\]         done clear
  B)
             \[\frac{n}{3}\] done clear
  C)
             \[n\sqrt{3}\]                         done clear
  D)
             \[\frac{n}{3\sqrt{3}}\] done clear
  View Solution play_arrow

• question_answer50)
  A string of length 2 m is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of 500 Hz then the waves would travel on its with a velocity of  [BCECE 2005]
  A)
             125 m/s                                   done clear
  B)
             250 m/s done clear
  C)
             500 m/s                                   done clear
  D)
             1000 m/s done clear
  View Solution play_arrow

• question_answer51)
  The fundamental frequency of a sonometre wire is n. If its radius is doubled and its tension becomes half, the material of the wire remains same, the new fundamental frequency will be                                          [BCECE 2005]
  A)
             n     done clear
  B)
             \[\frac{n}{\sqrt{2}}\] done clear
  C)
             \[\frac{n}{2}\]                      done clear
  D)
             \[\frac{n}{2\sqrt{2}}\] done clear
  View Solution play_arrow

• question_answer52)
  In an experiment with sonometer a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. Tension of the string remaining  constant  the frequency  of the second tuning fork is                                                                     [KCET 2005]
  A)
             163.84 Hz                                done clear
  B)
             400 Hz done clear
  C)
             320 Hz                                      done clear
  D)
             204.8 Hz done clear
  View Solution play_arrow