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# A transverse harmonic wave on a string is described by where x and y are in cm and t in s. The positive direction of x is from left to right.

Q.15.8 (a)  A transverse harmonic wave on a string is described by

$y(x,t)=3.0\; \sin (36\; t+0.018\; x+\pi /4)$

where x and y are in cm and t in s. The positive direction of x is from left to right.
(a) Is this a travelling wave or a stationary wave? If it is travelling, what are the speed and direction of its propagation?

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The wave is travelling.

$y(x,t)=Asin(kx+\omega t+\phi )$

The wave is travelling in the negative x-direction i.e. from right to left.

$\\\omega =36\ rad\ s^{-1}\\ k=0.018\ cm^{-1}$

Speed of the wave is

$\\v=\frac{\omega }{k}\\ v=\frac{36\times 10^{-2}}{0.018} \\v=20\ m\ s^{-1}$

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