The equation of a progressive wave is given by $y=4\sin \left\{\pi \left(\frac{{\displaystyle t}}{{\displaystyle 5}}-\frac{{\displaystyle x}}{{\displaystyle 9}}\right)+\frac{{\displaystyle \pi }}{{\displaystyle 6}}\right\}$.
Which of the following is correct​​​​?
1. v = 5 m / sec
2.  λ = 18 m
3.  a = 0.04 m
4.  n = 50 Hz

Two waves of frequencies 20 Hz and 30 Hz travel out from a common point. The phase difference between them after 0.6 sec is :

(1) Zero

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

(3) π

(4) $\frac{3\pi }{4}$

The equation of progressive wave is $y=a\sin (200t-x)$. where x is in meter and t is in second. The velocity of wave is :

(1) 200 m/sec

(2) 100 m/sec

(3) 50 m/sec

(4) None of these

A wave travelling in positive X-direction with A = 0.2 m has a velocity of 360 m/sec. if λ = 60 m, then the correct expression for the wave is :

(1) $y=0.2\sin \left[2\pi \left(6t+\frac{{\displaystyle x}}{{\displaystyle 60}}\right)\right]$

(2) $y=0.2\sin \left[\pi \left(6t+\frac{{\displaystyle x}}{{\displaystyle 60}}\right)\right]$

(3) $y=0.2\sin \left[2\pi \left(6t-\frac{{\displaystyle x}}{{\displaystyle 60}}\right)\right]$

(4) $y=0.2\sin \left[\pi \left(6t-\frac{{\displaystyle x}}{{\displaystyle 60}}\right)\right]$

A transverse progressive wave on a stretched string has a velocity of 10 ms^–1 and a frequency of 100 Hz. The phase difference between two particles of the string which are 2.5 cm apart will be :

(1) $\frac{\pi }{8}$

(2) $\frac{\pi }{4}$

(3) $\frac{3\pi }{8}$

(4) $\frac{\pi }{2}$

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

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

Tuning fork \(F_1\) has a frequency of 256 Hz and it is observed to produce 6 beats/second with another tuning fork \(F_2\). When \(F_2\) is loaded with wax, it still produces 6 beats/second with \(F_1\). The frequency of \(F_2\) before loading was:
1. 253 Hz
2. 262 Hz
3. 250 Hz
4. 259 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

Standing waves are produced in a 10 m long stretched string. If the string vibrates in 5 segments and the wave velocity is 20 m/s, the frequency is :

(1) 2 Hz

(2) 4 Hz

(3) 5 Hz

(4) 10 Hz