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 :

(1)zero                                 

(2)$\frac{2\mathrm{\pi }}{3}$

(3)$\mathrm{\pi }$                                     

(4)$\frac{\mathrm{\pi }}{6}$

A transverse wave is represented by y=$A \sin \left(\omega t-kx\right).$ For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

(1) $\mathrm{\pi } \mathrm{A}/2$                                           

(2) $\mathrm{\pi } \mathrm{A}$

(3) $2 \mathrm{\pi } \mathrm{A}$                                           

(4) A

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 $128 {\mathrm{ms}}^{-1}$ and it is noted that 5 complete waves fit in 4 m length of the string. The equation describing the wave is :

1. $y=\left(0.02\right)\mathrm{m} \sin \left(7.85\mathrm{x} +1005\mathit{ }t \right)$

2. $y=\left(0.02\right)\mathrm{m} \sin \left(15.7\mathrm{x} -2010\mathit{ }t \right)$

3. $y=\left(0.02\right)\mathrm{m} \sin \left(15.7\mathrm{x} +2010\mathit{ }t \right)$

4. $y=\left(0.02\right)\mathrm{m} \sin \left(7.85\mathrm{x} -1005\mathit{ }t \right)$

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 $g{m}^{-1}$When both the strings vibrate simultaneously the number of beats is :

1. 5                                                   

2. 7

3. 8                                                   

4. 3

Two periodic waves of intensities $I_1 and I_2$ pass through a region at the same time in the same direction. The sum of the maximum and  minimum intensities is :

1. $I_1+I_2$

2. ${\left(\sqrt{I_1}+\sqrt{I_2}\right)}^2$

3.${\left(\sqrt{I_1}-\sqrt{I_2}\right)}^2$

4. $2 \left(I_1+I_2\right)$ 

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?

1. $\frac{\pi }{3}$

2. $\frac{2\pi }{3}$

3. $\pi$

4. $\frac{\pi }{6}$

Two waves are represented by the equations $y_1=a\sin \omega t$ and $y_2=a\cos \omega t.$ The first wave 

(1) Leads the second by $\pi$

(2) Lags the second by $2\pi$

(3) Leads the second by $\frac{\pi }{2}$

(4) Lags the second by $\frac{\pi }{2}$

The distance between two consecutive crests in a wave train produced in a string is 5 cm. If 2 complete waves pass through any point per second, the velocity of the wave is :

1. 10 cm/sec

2. 2.5 cm/sec

3. 5 cm/sec

4. 15 cm/sec