Question 196: Waves

Question

A standing wave is formed by the superposition of two waves travelling in
opposite directions. The transverse displacement is given by
y(x, t) = 0.5 sin $$\left( {{{5\pi } \over 4}x} \right)\,$$ cos(200 $$\pi $$t).
What is the speed of the travelling wave moving in the positive x direction ?
(x and t are in meter and second, respectively.)

Accepted Answer

Standard equation of standing wave,
y(x, t) = 2a sin kx cos $$\omega $$t
Given,
y(x, t) = 0.5 sin $$\left( {{{5\pi } \over 4}x} ight)$$ cos (200$$\pi $$t).
So, k = $${{5\pi } \over 4}$$ and $$\omega $$ = 200$$\pi $$
$$	herefore\,\,\,$$ Speed of travelling wave
= $${\omega  \over k}$$ = $${{200\pi } \over {{{5\pi } \over 4}}}$$ = 160 m/s.

Answer

160 m/s

Answer

90 m/s

Answer

180 m/s

Answer

120 m/s

Waves

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