A transverse progressive wave on a stretched string has a velocity of 10 ms^–1 and a frequency of 100 Hz. The phase difference between two particles of the string which are 2.5 cm apart will be :

(1) $\frac{\pi }{8}$

(2) $\frac{\pi }{4}$

(3) $\frac{3\pi }{8}$

(4) $\frac{\pi }{2}$

The phase difference between two waves represented by $y_1={10}^{-6}\sin [100t+(x/50)+0.5]m,$ $y_2={10}^{-6}\cos [100t+(x/50\left)\right]m$ where x is expressed in metres and t is expressed in seconds, is approximately:

(1) 1.5 rad

(2) 1.07 rad

(3) 2.07 rad

(4) 0.5 rad

A particle on the trough of a wave at any instant will come to the mean position after a time (T = time period) 

(1) T/2

(2) T/4

(3) T

(4) 2T

When two sound waves with a phase difference of π/2, and each having amplitude A and frequency ω, are superimposed on each other, then the maximum amplitude and frequency of the resultant wave is :

(1) $\frac{A}{\sqrt{2}}:\frac{\omega }{2}$

(2) $\frac{A}{\sqrt{2}}:\omega$

(3) $\sqrt{2}A:\frac{\omega }{2}$

(4) $\sqrt{2}A:\omega$

The minimum intensity of sound is zero at a point due to two sources of nearly equal frequencies, when :

1. Two sources are vibrating in opposite phase

2. The amplitude of the two sources are equal

3. At the point of observation, the amplitudes of two S.H.M. produced by two sources are equal and both the S.H.M. are along the same straight line

4. Both the sources are in the same phase

Two sound waves (expressed in CGS units) given by $y_1=0.3\sin \frac{2\pi }{\lambda }(vt-x)$ and $y_2=0.4\sin \frac{2\pi }{\lambda }(vt-x+\theta )$ interfere. The resultant amplitude at a place where the phase difference is π/2 will be :

(1) 0.7 cm

(2) 0.1 cm

(3) 0.5 cm

(4) $\frac{1}{10}\sqrt{7}cm$

If two waves having amplitudes 2A and A and same frequency and velocity, propagate in the same direction in the same phase, the resulting amplitude will be 

1. 3A

2. $\sqrt{5}A$

3. $\sqrt{2}A$

4.  A

The intensity ratio of the two waves is 1 : 16. The ratio of their amplitudes is 

(1) 1 : 16

(2) 1 : 4

(3) 4 : 1

(4) 2 : 1

The superposing waves are represented by the following equations : $y_1=5\sin 2\pi (10t-0.1x)$, $y_2=10\sin 2\pi (20t-0.2x)$ Ratio of intensities $\frac{I_{\max }}{I_{\min }}$ will be :

(1) 1

(2) 9

(3) 4

(4) 16