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

Concept Questions :-

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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The driver of a car travelling with speed 30 ms-1 towards a hill sound a horn of frequency 600 Hz. If the velocity of sound in air is 330 ms-1, the frequency of reflected sound as heard by driver is 

(a) 550 Hz                             (b) 555.5 Hz

(c) 720 Hz                             (d) 500 Hz

Concept Questions :-

Doppler effect
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Each of the two strings of length 51.6 cm and 49.1 cm are tensioned separately by 20N force. Mass per unit length of both the strings is same and equal to 1 gm-1.When both the strings vibrate simultaneously the number of beats is :

(a) 5                                                    (b) 7

(c) 8                                                    (d) 3

Concept Questions :-

Standing waves
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