Question

A sinusoidal wave travelling in the positive $x$ direction has an amplitude of $15$ $cm$, wavelength $40$ $cm$ and frequency $8$ $Hz$. The vertical displacement of the medium at $t=0$ and $x=0$ is also $15$ $cm$ as shown. The wave number($k$), time period($T$), angular frequency($\omega$) and speed of the wave($v$) are

• A. $k=\frac{\pi }{20}rad/cm;T=\frac{1}{8}s;w=16s^{-1};v=320cm/s$
• B. $k=\frac{\pi }{20}rad/cm;T=\frac{1}{8}s;w=16s^{-1};v=160cm/s$
• C. $k=\frac{\pi }{20}rad/cm;T=\frac{1}{4}s;w=16s^{-1};v=320cm/s$
• D. $k=\frac{\pi }{10}rad/cm;T=\frac{1}{8}s;w=16s^{-1};v=320cm/s$

Answer 1

The correct option is A $k=\frac{\pi }{20}rad/cm;T=\frac{1}{8}s;w=16s^{-1};v=320cm/s$

$k=\frac{2\pi }{\lambda }=\frac{2\pi rad}{40cm}=\frac{\pi }{20}rad/cm$
$T=\frac{1}{f}=\frac{1}{8}s$ $\omega =2\pi f=16s^{-1}$
$v=f\lambda =320cm/s$