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

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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

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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

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Standing waves
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Two periodic waves of intensities  I1 and I2 pass through a region at the same time in the same direction. The sum of the maximum and  minimum intensities is :

(a) I1+I2

(b) I1+I22

(c)I1-I22

(d) 2 I1+I2 

 

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Two points are located at a distance of 10 m and 15 m from the source of oscillation. The period of oscillation is 0.05 s and the velocity of the wave is 300 m/s. What is the phase difference between the oscillations of two points?

(a) π3

(b) 2π3

(c) π

(d) π6

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The wave described by y=0.25 sin(10πx-2πt), where x and y are in metre and t in second, is a wave travelling along the 

(a) -ve x direction with frequency 1 Hz 

(b) +ve x direction with frequency π Hz and wavelength λ=0.2m 

(c) + ve x direction with frequency 1 Hz and wavelength λ=0.2 m

(d) - ve x direction with amplitude 0.25 m and wavelength λ=0.2 m

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