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

The displacement of a particle is given by $x=3\sin \left(5\pi t\right)+4\cos \left(5\pi t\right)$. The amplitude of the particle is :

(1) 3

(2) 4

(3) 5

(4) 7

The two interfering waves have intensities in the ratio 9 : 4. The ratio of intensities of maxima and minima in the interference pattern will be :

(1) 1 : 25

(2) 25 : 1

(3) 9 : 4

(4) 4 : 9

If the ratio of amplitude of two waves is 4 : 3. Then the ratio of maximum and minimum intensity will be :

(1) 16 : 18

(2) 18 : 16

(3) 49 : 1

(4) 1 : 49

Equation of motion in the same direction is given by $y_1=A\sin (\omega t-kx)$, $y_2=A\sin (\omega t-kx-\theta )$. The amplitude of the medium particle will be 

1. $2A\cos \frac{\theta }{2}$

2. $2A\cos \theta$

3. $\sqrt{2}A\cos \frac{\theta }{2}$

4. $1.2f,1.2\lambda$

The displacement of the interfering light waves are $y_1=4\sin \omega t$ and $y_2=3\sin \left(\omega t+\frac{{\displaystyle \pi }}{{\displaystyle 2}}\right)$. What is the amplitude of the resultant wave :

(1) 5

(2) 7

(3) 1

(4) 0

Two waves are represented by $y_1=a\sin \left(\omega t+\frac{{\displaystyle \pi }}{{\displaystyle 6}}\right)$ and $y_2=a\cos \omega t$. What will be their resultant amplitude :

(1) a

(2) $\sqrt{2}a$

(3) $\sqrt{3}a$

(4) 2a