A transverse harmonic wave on a string is described by `y ( x,t )= 30 sin ( 36 t + 0.018x + ( pi)/(4) ) `where x and y are in cm and t is in s.The positive direction of x is from left to right.
Is this a travelling wave or a stationary wave ? If it is travelling, what are the speed and direction of its propagation ?

Explanation

Given, `y ( x,t) = 3.0 sin ( 36 t +0.018 x + ( pi)/(4))`
Standard format for a stationary wave is `y = f(x)g(t)` . Since the given wave has`y = f( x,t),` the equation represents a progressive wave.
Speed of the wave `v =( omega )/( k ) = (36)/( 0.018) =2000cms^(-1) ` or `v = 20 ms^(-1)`
The progressive wave is travelling from right to left.