Question

A person has a hearing range from 20 Hz to 20 kHz. What are the typical wavelengths of sound waves in air corresponding to these two frequencies? Take the speed of sound in air as 344 m/s.

Answer 1

Step 1- Given data

The speed of sound in air $v=344m/s$

Hearing range i.e. $20Hzto20kHz$

Step 2- Finding wavelength regarding 20 Hz frequency

For a sound wave-

Speed (ν ) = Wavelength (λ) x Frequency(f)

$v=f_1{\lambda }_1$

$$\begin{gathered} f_1=20Hz \\ \Rightarrow {\lambda }_1=\frac{v}{f_1} \\ \Rightarrow {\lambda }_1=\frac{344}{20} \\ \Rightarrow {\lambda }_1=17.2m \end{gathered}$$

Step 3- Finding wavelength regarding 20 kHz frequency

$v=f_2{\lambda }_2$

$$\begin{gathered} \Rightarrow {\lambda }_2=\frac{v}{f_2} \\ \Rightarrow {\lambda }_2=\frac{344}{20000} \\ \Rightarrow {\lambda }_2=0.0172m \end{gathered}$$

Hence, for humans, the wavelength range for hearing is$0.0172mto17.2m.$