Chapter 22, Problem 112A

To determine

The wavelength of a sound wave in air.

Answer to Problem 112A

The wavelength of the sound wave is $20.17\text{mm}$.

Explanation of Solution

Given:

Sound wave with a frequency of 17-kHz is traveling in air

Formula used:

The wavelength of any wave is a function of its frequency f and velocity v, which can be expressed mathematically as

  $\lambda =\frac{v}{f}$.......(1)

Calculation:

Here, the sound wave is considered and it is traveling in air. The velocity of sound in air considering room temperature, is $\text{343 m/s}$ and the frequency is $17\text{ kHz}$ .

Substituting these parameters in (1), the wavelength of sound in air is obtained as,

  $\begin{array}{c}\lambda =\frac{343}{17\times {10}^3}\\ =20.17\text{ mm}\end{array}$

Conclusion:

The wavelength of sound with a particular frequency, in air is 20.17 mm.