Chapter 12, Problem 3P

(a) Calculate the wavelengths in air at 20°C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. (b) What is the wavelength of an 18-MHz ultrasonic wave?

To determine

The range of wavelength.

Answer to Problem 3P

Solution:

The range of wavelength will be$17m$ and wavelength of a $18-mhz$ ultrasonic wave.

Explanation of Solution

Given:

  $\begin{array}{l}{f}_1=20hz\\ f_2=20,000hz\\ T={20}^{0}c\\ v=343m/s\end{array}$

(a) $v=f\lambda$

Calculate the wavelength corresponding to $20hz$

$\lambda =\frac{v}{f}$

$\begin{array}{l}{\lambda }_{20hz}=\frac{343m/s}{20hz}\\ =17m\end{array}$

Calculate the wavelength corresponding to$20,000hz$

$\begin{array}{l}\lambda =\frac{343m/s}{2.0\times {10}^{4}hz}\\ =1.7\times {10}^{-2}\\ =1.7cm\end{array}$

The range of wavelength is

$1.7cmto17m$

(b)wave length of an $18mhz$ ultrasonic wave

${\lambda }_{18mhz=}\frac{343m/s}{18\times {10}^{6}hz}=19\mu m$