Question

A travelling harmonic wave on a string is describe by y = 7 sin $(12t+0.005x+\frac{\pi }{4})$, where X and Y are in cm and t is in s.

1. Calculate particle velocity at X = 1 cm and t = 1s

2. Determine frequency

3. Initial phase at origin.

4. Amplitude

Answer 1

Given that,

$y=7\sin (12t+0.005x+\frac{\pi }{4})$

Now, the speed of the wave when $x=1m$ and $t=1s$

$v=\frac{\omega }{k}$

$v=\frac{12}{0.005}$

$v=2400cm/s$

$v=24m/s$

Now the initial phase at origin

$\varphi =\frac{\pi }{4}$

Now, the frequency is

$f=\frac{\omega }{2\pi }$

$f=\frac{12}{2\pi }$

$f=1.9Hz$

Now, the amplitude is

$A=7cm$
this is answer