Two sources of sound placed close to each other, are emitting progressive waves given by

y1=4 sin 600πt and y2=5 sin 608 πt

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

(b) 8 beats per second with intensity ratio 25:16 between waxing and waning

(c) 8 beats per second with intensity ratio 81:1 between waxing and waning

(d) 4 beats per second with intensity ratio 81:1 waxing and waning

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The equation of a simple harmonic wave is 

given by 

          y=3 sinπ2(50t-x)

where x and y are in meters and t is in 

seconds. The ratio of maximum particle 

velocity to the wave velocity is

(a) 2π

(b) 32π

(c) 3π

(d) 23π

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Speed of sound
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A train moving at a speed of 220 ms-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 330 ms-1)

(a) 3500Hz

(b) 4000Hz

(c) 5000Hz

(d) 3000Hz

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Doppler effect
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Two waves are represented by the equations y1=a sin (ωt+kx+0.57)m and y2=a cos (ωt+kx)m, where x is in metre and t in second. The phase difference between them is?

(a) 1.25 rad

(b) 1.57 rad

(c) 0.57 rad

(d) 1.0 rad

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Sound waves travel at 350 m/s through a warm 

air and at 3500 m/s through brass. The wavelength

of a 700 Hz acoustic wave as it enters brass from 

warm air :

(a) increases by factor 20

(b) increases by factor 10

(c) decreases by factor 20

(d) decreases by factor 10

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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 the occurrence of 6 beats/s when both the wires oscillate together would be :

(a) 0.02                                            (b) 0.03

(c) 0.04                                             (d) 0.01 

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Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is :

(a)zero                                  (b)2π3

(c)π                                      (d)π6

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A transverse wave is represented by y=A sin ωt-kx. For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

(a) π A/2                                           (b) π A

(c) 2 π A                                            (d) A

Concept Questions :-

Types of waves
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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

(a) 510 Hz                        (b) 514 Hz

(c) 516 Hz                        (d) 508 Hz

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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 ms-1 and it is noted that 5 complete waves fit in 4 m length of the string. The equation describing the wave is :

(a) y=0.02m sin 7.85x +1005 t 

(b) y=0.02m sin 15.7x -2010 t 

(c) y=0.02m sin 15.7x +2010 t 

(d) y=0.02m sin 7.85x -1005 t 

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