Question

A sound wave travels at a speed of $399m{s}^{-1}$. If its wavelength is $1.5m$, what is the frequency of the wave? Will it be audible?

Answer 1

Step 1: Given data.

Speed of sound wave, $v=399m{s}^{-1}$

Wavelength, $\lambda =1.5m$

Frequency, $f=?$

Step 2: Calculate the frequency.

The frequency is calculated below:

$\begin{array}{rcl}f& =& \frac{v}{\lambda }\\ & \Rightarrow & f=\frac{399m{s}^{-1}}{1.5m}\\ & \Rightarrow & f=266Hz\end{array}$

Step 3: Determine whether the obtained frequency will be audible or not.

1. Sound waves of the frequency range between $20Hz\text{to}20,000Hz$ is audible by the human ear.
2. The frequency obtained is $266Hz$. It lies between $20Hz\text{and}20,000Hz$, so it will be audible.

Hence, the frequency of the wave is $266Hz$ and it will be audible.