Chapter 26, Problem 44A

To determine

The wavelength of a sound wave with a frequency of 20 Hz and wavelength of a sound wave with a frequency of 20 kHz.

Answer to Problem 44A

The wavelength of a sound wave with a frequency of 20 Hz is 17 m and wavelength of a sound wave with a frequency of 20 kHz is $1.7\times 10^{-2}m$ .

Explanation of Solution

Given:

Speed of sound wave ( $\mathrm{s}$ ) = $340m{s}^{-1}$

  $\mathrm{frequency}(f_1)=20Hz$

  $\mathrm{frequency}(f_2)=20,000Hz$

Formula used:

  $\begin{array}{l}\mathrm{speed}(s)=frequency(f)\times wavelength(\lambda )\\ wavelength(\lambda )=\frac{\mathrm{speed}(s)}{frequency(f)}\end{array}$

Calculation:

For $\mathrm{frequency}(f_1)=20Hz$

Put the given values and we get;

  $\begin{array}{l}\mathrm{wavelength}({\lambda }_1)=\frac{340m{s}^{-1}}{20Hz}=17m\\ {\lambda }_1=17m\end{array}$

For $\mathrm{frequency}(f_2)=20,000Hz$

Put the given values and we get;

  $\begin{array}{l}\mathrm{wavelength}({\lambda }_2)=\frac{340m{s}^{-1}}{20,000Hz}=1.7\times {10}^{-2}m\\ {\lambda }_2=17\times {10}^{-2}m\end{array}$

Conclusion:

Thus, the wavelength of a sound wave with a frequency of 20 Hz is 17 m and wavelength of a sound wave with a frequency of 20 kHz is $1.7\times 10^{-2}m$ .