A wave travelling in positive X-direction with A = 0.2 m has a velocity of 360 m/sec. if λ = 60 m, then the correct expression for the wave is :

(1) $y=0.2\sin \left[2\pi \left(6t+\frac{{\displaystyle x}}{{\displaystyle 60}}\right)\right]$

(2) $y=0.2\sin \left[\pi \left(6t+\frac{{\displaystyle x}}{{\displaystyle 60}}\right)\right]$

(3) $y=0.2\sin \left[2\pi \left(6t-\frac{{\displaystyle x}}{{\displaystyle 60}}\right)\right]$

(4) $y=0.2\sin \left[\pi \left(6t-\frac{{\displaystyle x}}{{\displaystyle 60}}\right)\right]$

Two waves represented by the following equations are travelling in the same medium $y_1=5\sin 2\pi (75t-0.25x)$, $y_2=10\sin \pi (150t-0.50x)$

The intensity ratio I₁/I₂ of the two waves is :

(1) 1 : 2

(2) 1 : 4

(3) 1 : 8

(4) 1 : 16

Which of the following is not true for this progressive wave $y=4\sin 2\pi \left(\frac{{\displaystyle t}}{{\displaystyle 0.02}}-\frac{{\displaystyle x}}{{\displaystyle 100}}\right)$ where y and x are in cm and t in sec 

(1) Its amplitude is 4 cm

(2) Its wavelength is 100 cm

(3) Its frequency is 50 cycles/sec

(4) Its propagation velocity is 50 × 10³ cm/sec

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