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

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

The amplitude of a wave represented by displacement equation $y=\frac{1}{\sqrt{a}}\sin \omega t\pm \frac{1}{\sqrt{b}}\cos \omega t$ will be

(1) $\frac{a+b}{ab}$

(2) $\frac{\sqrt{a}+\sqrt{b}}{ab}$

(3) $\frac{\sqrt{a}\pm \sqrt{b}}{ab}$

(4) $\sqrt{\frac{a+b}{ab}}$

When a tuning fork of frequency 341 is sounded with another tuning fork, six beats per second are heard. When the second tuning fork is loaded with wax and sounded with the first tuning fork, the number of beats is two per second. The natural frequency of the second tuning fork is :

(1) 334

(2) 339

(3) 343

(4) 347

When two sound waves are superimposed, beats are produced when they have :

(1) Different amplitudes and phases

(2) Different velocities

(3) Different phases

(4) Different frequencies

It is possible to hear beats from the two vibrating sources of frequency :

(1) 100 Hz and 150 Hz

(2) 20 Hz and 25 Hz

(3) 400 Hz and 500 Hz

(4) 1000 Hz and 1500 Hz

Two vibrating tuning forks produce progressive waves given by $Y_1=4\sin 500\pi t$ and $Y_2=2\sin 506\pi t.$ Number of beats produced per minute is :

(1) 360

(2) 180

(3) 3

(4) 60

A wave represented by the given equation $y=a\cos (kx-\omega t)$ is superposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation for the other wave is :

(1) $y=a\sin (kx+\omega t)$

(2) $y=-a\cos (kx+\omega t)$

(3) $y=-a\cos (kx-\omega t)$

(4) $y=-a\sin (kx-\omega t)$

A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance 1.21 Å between them. The wavelength of the standing wave is :

(1) 1.21 Å

(2) 2.42 Å

(3) 6.05 Å

(4) 3.63 Å