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

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

Two tuning forks when sounded together produced 4 beats/sec. The frequency of one fork is 256 Hz. The number of beats heard increases when the fork of frequency 256 Hz is loaded with wax. The frequency of the other fork is(in Hz) :

(1) 504

(2) 520

(3) 260

(4) 252

A tuning fork sounded together with a tuning fork of frequency 256 Hz emits two beats. On loading the tuning fork of frequency 256 Hz with wax, the number of beats heard are 1 per second. The frequency of the other tuning fork is :

(1) 257

(2) 258

(3) 256

(4) 254

If two tuning forks A and B are sounded together, they produce 4 beats per second. A is then slightly loaded with wax, they produce 2 beats when sounded again. The frequency of A is 256. The frequency of B will be :

(1) 250

(2) 252

(3) 260

(4) 262