Define standing wave. Displacement of a string in which standing … - Vidyadip

Question

Define standing wave. Displacement of a string in which standing wave is formed is given as $\text{y}=(20\sin157\text{x}\cos314\text{t})$ Find:

Amplitude of individual waves.
Velocity of wave.

✓

Answer

A standing wave is a pattern generated due to the superposition of two waves moving in opposite direction. It has varying amplitude.
$\text{Y} =20\sin157\text{x}\cos314\text{t}$
On comparison with $\text{Y}=2\text{A}\sin\text{kx}\cos\omega\text{t}$
We have,

Amplitude = 10 units.
Velocity of wave $=\frac{\omega}{\text{k}}=\frac{314}{157}=2\text{ units}.$

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