The transverse displacement of a string is given by `y ( x , t ) = 0.06 sin ((2pi)/(3)) x cos ( 120 pi t)` where 'x' & 'y' are 'm' and 't' is s. The length of the string is 1.5m and its mass is `3.0 xx 10^(-2) kg`.
Interpret the wave as a superposition of two waves travelling in opposite direction. What is the wavelength, frequency and speed of each wave?

Explanation

The given equation is,
`y( x,t) =0.06 sin ((2pi)/(3))x cos(120pit)`comparing this with
Consider two waves of `y_(1) = Asin (kx +omega t ) ` and `y_(2) = A sin ( kx-omegat)` superpose with each other.The combined wave has a displacement `y =y_(1) + y_(2) =A[sin ( kx+omega t ) + sin ( kx-omega t )]`
`y =2A sin kx cos omegat ` which represents a stationary wave.
Comparing the equation ,
`kx = ((2pi)/(3)) x ` i.e., ` ( 2pi)/( lambda ) = (2pi )/( 3)`
Hnce `lambda = 3m` and `omegat =120 pi t, 2pi f t ` or ` f=60 Hz`,
Speed of individual waves `v = f lambda`
`v = 60 xx 3`
`v =180ms^(-1)`