Question

Velocity of sound waves in air is $330m/sec$. For a particular sound in air, a path difference of $40cm$ is equivalent to a phase difference of $1.6$$\pi$. The frequency of this wave is

• A. $165Hz$
• B. $150Hz$
• C. $660Hz$
• D. $330Hz$

Answer 1

Answer: (C)

$660Hz$

Velocity of sound waves $=330m/s$

$\Delta \varphi =K\Delta x$

where, $\Delta =$ Phase difference

$K=\frac{2\pi }{\lambda }$

where, $\Delta x=$ Path difference

Putting the values given in question,

$1.6\pi =\frac{2\pi }{\lambda }\frac{40}{100}$

$\lambda =\frac{2\pi }{1.6\pi }\times \frac{40\times 10}{100}=\frac{1}{2}m$

Now,

$V=\frac{f}{\lambda }$

$330=f\frac{1}{2}$

$f=660Hz$