Question

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by $y = (10 cos \ \pi x\ sin \frac {2\pi t}{T})$ cm. The amplitude of the particle at $x = \frac 43$ cm will be _______ cm.

Answer 1

$A = | 10 cos (\pi x)$
At $x = \frac 43$
$A = | 10 cos (\pi \times \frac 43) |$
$A = | 10\ cos (240^o) |$
$A = | 10 \times \frac {-1}{2}) |$
$A= | -5\ cm |$

Therefore, amplitude = $5\ cm$.