Question

The phase difference between two points separated by $0.8\text{m}$ in a wave of frequency $120\text{Hz}$ is $0.5\pi$. The velocity of wave will be

• A. $720\text{m/s}$
• B. $384\text{m/s}$
• C. $256\text{m/s}$
• D. $144\text{m/s}$

Answer 1

The correct option is B $384\text{m/s}$

Given:
Path difference, $\Delta x=0.8\text{m}$
Phase difference resulting due to path difference is given by,
$\Delta \varphi =\frac{2\pi }{\lambda }\times \Delta x$
$\Rightarrow 0.5\pi =\frac{2\pi }{\lambda }\times 0.8$
$\Rightarrow \lambda =3.2\text{m}$
Now, wave velocity,
$v=f\lambda$
$\Rightarrow v=120\times 3.2=384\text{m/s}$