Question

Most people can detect frequencies as high as $20000Hz$. Assuming the speed of sound in air to be $345m{s}^{-1}$, determine the wavelength of sound corresponding to this upper range of audible hearing.

Answer 1

Step 1:Given Data:

Frequency of the highest detectable frequency by the human ear, $f=20000Hz$

Speed of sound waves in the air, $v=345m{s}^{-1}$

Step 2: Formula & solution:

The frequency ($f$) of a wave is the number of complete wave cycles in unit time.

The wavelength ($\lambda$) of a wave is the distance covered by a wave in a complete wave cycle.

The speed ($\nu$) of a wave is the distance covered by the wave in unit time.

The speed ($\nu$) of the wave is related to the wavelength ($\lambda$) and frequency ($f$) of the wave as follows:

$$\begin{gathered} \nu =\lambda \times f \\ \lambda =\frac{\nu }{f} \end{gathered}$$

Step 3: Determine the wavelength:

Putting the values of maximum detectable frequency ($f$) and speed ($\nu$), we can determine the wavelength corresponding to maximum frequency:

$$\begin{gathered} \lambda =\frac{345}{20000}m \\ =1.725\times {10}^{-2}m \\ =1.725cm \end{gathered}$$

Therefore, the wavelength associated with the maximum detectable frequency is $1.725cm$.