Question

The vibrations of a string of length $60cm$ fixed at both ends are represented by the equation $y=4\sin \left(\frac{\pi x}{15}\right)\cos \left(96xt\right)$
where $x$ and $y$ are in cm and in seconds

• A. what is the maximum displacement of a point at $x=5cm$?
• B. where are the nodes located along the string?
• C. what is the velocity of the particle at $x=7.5cm$ at $t=0.25sec$?
• D. write down the equations of the component waves whose superposition gives the above wave.

Answer 1

The correct option is A what is the maximum displacement of a point at $x=5cm$?

Equation of standing wave is of the form

$\Rightarrow y=A\sin \left(kx\right)ws\left(wt\right)$

There should be no term of $ws\left(kxt\right).$

Hence, solved.