A transverse harmonic wave on a string is described by `y(x,t)=3.0sin(36t+0.018x+pi//4)` where x, y are in cm, t in second. The positive direction of x is from left to right . (i) Is this a travelling or stationary wave ? If travellying, what are the speed and direction of its propagation ? (ii) what are its amplitude and frequency ? (iii) what is the inital phase at the origing ? (iv) What is the least distance between two successive creests in the wave?

Options

A. the wave is travelling from right to left
B. the speed of the wave is 20 m/s
C. frequecny of the wave is 5.7 Hz
D. the least distance between two successive crests in the wave is 2.5 cm

Answer

A, B, C

Explanation

Given equation is `" " y(x,t)=3.0sin(36t+0.018x+(pi)/(4))`
Compare the eqution with the standard form
`" " y= a sin theta (omega t+kx+phi)`
(a) As the equation in equation involves positive sign with x, hence the wave is travelling from right to left, Hence, option (a) is correct .
(b) Givne `" " omega=36rArr2piv=36`
` rArr" " ` v=frequency `=(36)/(2pi)=(18)/(pi)`
`" " k=0.018 rArr(2pi)/(lambda)=0.018`
`rArr " " (2piv)/(vlambda)=0.018rArr(omega)/(v)=0.018" " [ :. 2piv=omega and v lambda=v]`
`rArr" " (36)/(v)=0.018=(18)/(1000)`
`rArr" " v=200 cm//s =20 m//s`
(c) `2piv=36`
` rArr" v=(36)/(2pi)Hz=(18)/(pi) =5.7 Hz`
(d) `(2i)/(lambda)=0.018`
`rArr" " lambda=(2pi)/(0.018)cm`
`" " =(2000pi)/(18)cm=(20pi)/(18)m=3.48 cm`
Hence least distane between two successinve crests `=lambda=3.48m`