Question

A sound wave travels at a speed of $339m/s$. If its wavelength is \[1.5cm\], what is the frequency of the wave?
\[\begin{align}
  & A.2600Hz \\
 & B.2200HZ \\
 & C.2260Hz \\
 & D.22600Hz \\
\end{align}\]

Answer 1

Hint: We know that the sound waves are produced due to the vibration of the particles of the medium through which they propagate. Then clearly since sound is a wave, it has some frequency, wavelength and speed. They are interrelated to each other.

Formula used:
$\nu=\dfrac{s}{\lambda}$

Complete step-by-step answer:
We know that sound waves are both transverse and longitudinal waves. Also, the sound waves are caused due to the vibrations or oscillation of the particles of the sound wave in any given medium. And the nature of propagation of sound waves depends on the medium. We are able to perceive sound when these vibrations reach our ears and cause our eardrums to vibrate. Also the vocal cords are needed to produce sounds. Thus clearly sound is an energy which produces a sense of hearing.
Here, it is given that the speed of the wave is $339m/s$, and the wavelength of the wave is \[1.5cm\]
We also know that $s=\nu\lambda$ for waves, where $\lambda$ is the wavelength if the wave whose speed is $s$ any medium and frequency is $\nu$. Then rearranging we get, $\nu=\dfrac{s}{\lambda}$
Substituting the values, we $\nu=\dfrac{339}{1.5\times 10^{-2}}=22.6kHz$
Clearly, this is greater than the audible frequency range $20-20kHz$, and hence is not audible.
However, the required answer is $f=22.6kHz$

So, the correct answer is “Option C”.

Note: The energy of a sound wave is given as $E=h\nu$ where $h$ is the Planck’s constant and $\nu$ is the frequency of the wave. We humans can perceive sound whose frequency is of the range $20-20kHz$. Anything above or below this range our ears cannot perceive them. Any sound above \[20kHz\] is called ultrasound which is used by bats and whales for communications. And sounds below \[20Hz\] are called infrasound.