A simple harmonic progressive wave is represented by the equation : $y=8\sin 2\pi (0.1x-2t)$ where x and y are in cm and t is in seconds. At any instant the phase difference between two particles separated by 2.0 cm in the x-direction is :

(1) 18°

(2) 36°

(3) 54°

(4) 72°

A wave equation that gives the displacement along y-direction is given by $y=0.001\sin (100t+x)$ where x and y are in meter and t is time in seconds. This represented a wave :

(1) Of frequency $\frac{100}{\pi }$Hz

(2) Of wavelength one metre

(3) Traveling with a velocity of $\frac{50}{\pi }$ms^–1 in the positive X-direction

(4) Traveling with a velocity of 100 ms^–1 in the negative X-direction

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 × ${10}^4$ cm/sec

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