Question

The standing waves set upon a string are given by
$y=4\sin \left(\frac{\pi x}{12}\right)\cos \left(52\pi t\right)$
If $x$ and $y$ are in centimetres and $t$ is in seconds, what is the amplitude of the particle at $x=2cm$?

• A. $12cm$
• B. $4cm$
• C. $2cm$
• D. $1cm$

Answer 1

Answer: (C)

$2cm$

Putting $x=2$ cm in the given standing wave equation, we get $y=4\sin \left(\frac{\pi }{6}\right)\sin \left(52\pi t\right)=2\sin \left(52\pi t\right)$.
Thus, the amplitude is $2cm$