JEE Main & Advanced Physics Wave Mechanics Question Bank

done Mock Test - Waves and Acoustics Total Questions - 25

• question_answer1)
  Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneously. On changing the tension in one of them, the beat frequency remains unchanged. Denoting by \[{{T}_{1}}\], \[{{T}_{2}}\], the higher and the lower initial tensions in the strings, then it could be said that while making the above change in tension
  A)
  \[{{T}_{2}}\] was decreased       done clear
  B)
  \[{{T}_{2}}\]was increased done clear
  C)
  \[{{T}_{1}}\] was increased        done clear
  D)
  \[{{T}_{1}}\]was kept constant done clear
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• question_answer2)
  An open pipe is in resonance in its \[{{2}^{nd}}\] harmonic with tuning fork of frequency\[{{f}_{1}}\]. Now it is closed at one end. If the frequency of the tuning fork is increased slowly from \[{{f}_{1}}\] then again a resonance is obtained with a frequency\[{{f}_{2}}\]. If in this case the pipe vibrates \[{{n}^{th}}\] harmonics then
  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)
  \[n=5,\,\,{{f}_{2}}=\frac{5}{4}{{f}_{1}}\]       done clear
  D)
  \[n=5,\,\,{{f}_{2}}=\frac{3}{4}{{f}_{1}}\] done clear
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• question_answer3)
  Vibrating tuning fork of frequency n is placed near the open end of a long cylindrical tube. The tube has a side opening and is fitted with a movable reflecting piston. As the piston is moved through   8.75 cm, the intensity of sound changes from a maximum to minimum. If the speed of sound is 350 m/s. Then n is
  A)
  500 Hz  done clear
  B)
  1000 Hz done clear
  C)
  2000 Hz done clear
  D)
  4000 Hz done clear
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• question_answer4)
  A stone is hung in air from a wire which is stretched over a sonometer. The bridges of the sonometer are \[L\] cm apart when the wire is in unison with a tuning fork of frequency\[N\]. When the stone is completely immersed in water, the length between the bridges is \[l\] cm for re-establishing unison, the specific gravity of the material of the stone is
  A)
  \[\frac{{{L}^{2}}}{{{L}^{2}}+{{l}^{2}}}\] done clear
  B)
  \[\frac{{{L}^{2}}-{{l}^{2}}}{{{L}^{2}}}\] done clear
  C)
  \[\frac{{{L}^{2}}}{{{L}^{2}}-{{t}^{2}}}\]  done clear
  D)
  \[\frac{{{L}^{2}}-{{l}^{2}}}{{{L}^{2}}}\] done clear
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• question_answer5)
  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 seconds, 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_answer6)
  A source of sound of frequency\[{{f}_{1}}\] is placed on the ground. A detector placed at a height is released from rest on this source. The observed frequency\[{{f}_{{}}}(Hz)\] is plotted against time \[t\](sec). The speed of sound in air is 300 m/s. Find\[{{f}_{1}}\]\[(g=10m/{{s}^{2}})\]
  A)
  \[0.5\times {{10}^{3}}Hz\]        done clear
  B)
  \[1\times {{10}^{3}}Hz\] done clear
  C)
  \[0.25\times {{10}^{3}}\]          done clear
  D)
  \[0.25\times {{10}^{3}}Hz\] done clear
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• question_answer7)
  When beats are produced by two progressive waves of nearly the same frequency, which one of the following is correct?
  A)
  The particles vibrate simple harmonically, with the frequency equal to the difference in the component frequencies. done clear
  B)
  The amplitude of vibration at any point changes simple harmonically with a frequency equal to the difference in the frequencies of the two waves. done clear
  C)
  The frequency of beats depends upon the position, where the observer is. done clear
  D)
  The frequency of beats changes as the time progresses. done clear
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• question_answer8)
  Which of the following statements is correct for stationary waves?
  A)
  Nodes and antinodes are formed in case of stationary transverse wave only done clear
  B)
  In case of longitudinal stationary wave, compressions and rarefactions are obtained in place of nodes and antinodes respectively done clear
  C)
  Suppose two plane waves, one longitudinal and the other transverse having same frequency and amplitude are travelling in a medium in opposite directions with the same speed, by superposition of these waves, stationary waves cannot be obtained done clear
  D)
  None of the above done clear
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• question_answer9)
  A string is under tension so that its length is increased by \[1/n\] times its original length. The ratio of fundamental frequency of longitudinal vibrations and transverse vibrations will be
  A)
  \[1:n\]                done clear
  B)
  \[{{n}^{2}}:1\] done clear
  C)
  \[\sqrt{n}:1\]      done clear
  D)
  \[n:1\]   done clear
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• question_answer10)
  A closed organ pipe and an open organ pipe of same length produce 2 beats when they are set into vibration simultaneously in their fundamental mode. The length of the open organ pipe is now halved and of the closed organ pipe is doubled; the number of beats produced will be
  A)
  8                      done clear
  B)
  7 done clear
  C)
  4                      done clear
  D)
  2 done clear
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• question_answer11)
  The linear density of a vibrating string is\[{{10}^{-4}}kg/m\]. A transverse wave is propagating on the string, which is described by the equation\[y=0.02\sin (x+30t)\], where \[x\] and\[y\] are in metres and time \[t\] in seconds. Then tension in the string is
  A)
  0.09 N   done clear
  B)
  0.36 N done clear
  C)
  0.9 N    done clear
  D)
  3.6 N done clear
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• question_answer12)
  In sports meet the timing of a 200 m straight dash is recorded at the finish point by starting an accurate stop watch on hearing the sound of starting gun fired at the starting point. The time recorded will be more accurate
  A)
  In winter            done clear
  B)
  In summer done clear
  C)
  In all seasons      done clear
  D)
  None of these done clear
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• question_answer13)
  The equations of a travelling and stationary waves are \[{{y}_{1}}=a\sin (\omega t-kx)\] and\[{{y}_{2}}=a\sin \,kx\,cos\,\omega t\]. The phase differences between two points \[{{x}_{1}}=\frac{\pi }{4k\,}\,and\,{{x}_{2}}=\frac{4\pi }{3k}\] are \[{{\phi }_{1}}\] and \[{{\phi }_{2}}\] respectively for two waves, where k is the wave number. The ratio of \[{{\phi }_{1}}/{{\phi }_{2}}\] is
  A)
  6/7                    done clear
  B)
  16/3 done clear
  C)
  12/13    done clear
  D)
  13/12 done clear
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• question_answer14)
  A tuning fork produces 4 beats per second with another fork of frequency 288 cps. A little wax is placed on the unknown fork and it then produces 2 beats per second. The unknown frequency is
  A)
  286 cps done clear
  B)
         284 cps done clear
  C)
  292 cps done clear
  D)
         290 cps done clear
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• question_answer15)
  A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
  A)
  256 + 5 Hz        done clear
  B)
  256 + 2 Hz done clear
  C)
  256 - 2 Hz         done clear
  D)
  256 - 5 Hz done clear
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• question_answer16)
  While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, he measures the column length to be \[x\] centimeter for the second resonance. Then
  A)
  18 >\[x\]           done clear
  B)
  \[x\]>54 done clear
  C)
  54>\[x\]>36      done clear
  D)
  36>\[x\]>18 done clear
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• question_answer17)
  The equation of a wave on a string of linear mass density 0.04 kg/m is given by\[y=0.02(m)sin\left[ 2\pi \left( \frac{t}{0.04(s)}-\frac{x}{0.50(m)} \right) \right]\] 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_answer18)
  A person is standing at a distance \[D\] from an isotropic point source of sound. He walks 50.0 m towards the source and observes that the intensity of the sound has doubled. His initial distance \[D\] from the source is
  A)
  \[50\sqrt{2}m\]   done clear
  B)
  \[\frac{50\sqrt{2}}{\sqrt{2}-1}m\] done clear
  C)
  \[\frac{50}{\sqrt{2}-1}m\]           done clear
  D)
  \[100\sqrt{2}m\] done clear
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• question_answer19)
  How long will it take sound waves to travel a distance between points \[A\] and \[B\] if the air temperature between them varies linearly from \[{{T}_{1}}\] to\[{{T}_{2}}\]? (The velocity of sound in air at temperature T is given by \[v=\alpha \sqrt{t}\], where a is \[a\] constant)
  A)
  \[\frac{2l}{\alpha \sqrt{{{T}_{1}}{{T}_{2}}}}\]             done clear
  B)
  \[\alpha l\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\] done clear
  C)
  \[\sqrt{{{T}_{1}}+{{T}_{2}}}.\alpha l\]            done clear
  D)
  \[\frac{2l}{\alpha (\sqrt{{{T}_{2}}+\sqrt{{{T}_{1}}}})}\] done clear
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• question_answer20)
  Two sources \[{{S}_{1}}\] and \[{{S}_{2}}\] of same frequency\[f\]emits sound. The sources are moving as shown with speed \[u\] each. A stationary observer hears that sound. The beat frequency is (\[v\] = velocity of sound)
  A)
  \[\frac{2{{u}^{2}}f}{{{v}^{2}}-{{u}^{2}}}\]           done clear
  B)
  \[\frac{2{{v}^{2}}f}{{{v}^{2}}-{{u}^{2}}}\] done clear
  C)
  \[\frac{2\,u\,vf}{{{v}^{2}}-{{u}^{2}}}\]         done clear
  D)
  \[\frac{2u}{v}f\] done clear
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• question_answer21)
  A wire of density \[9\times {{10}^{3}}kg/{{m}^{3}}\] is stretched between two clamps 1 m apart and is subjected to an extension of \[4.9\times {{10}^{-4}}\] m. What is the lowest frequency (in Hz) of transverse vibration in the wire?
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• question_answer22)
  The difference between the apparent frequency of a source of sound as perceived by an observer during its approach and recession is 2% of the natural frequency of the source. If the velocity of sound in air is 300 m/sec, what is the velocity (in m/s) of the source? (It is given that velocity of source << velocity of sound)
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• question_answer23)
  Two identical sounds \[{{S}_{1}}\] and \[{{S}_{2}}\] reach at a point \[P\] in phase. The resultant loudness at point P is \[n\] dB higher than the loudness of\[{{S}_{1}}\]. What is the value of\[n\]?
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• question_answer24)
  Wavelengths of two notes in air are 1 m and\[\frac{1}{164}\]m. Each note produces 1 beat/s with a third note of a fixed frequency. What is the speed (in m/s) of sound in air?
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• question_answer25)
  The displacement\[y\]of a particle executing periodic motions given by\[y=4{{\cos }^{2}}\frac{t}{2}\sin 1000t\] How many independent harmonic motions may be considered to superpose to result this expression.            
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