Question

Ultrasound is the name given to frequencies above the human range of hearing, which is about 20,000 Hz. Waves above this frequency can be used to penetrate the body and produce images by reflecting from surfaces. In a typical ultrasound scan, the waves travel with a speed of 1,809 m/s. For a good detailed image, the wavelength should be no more than 1.44 mm. What frequency is required?

Answer 1

Concepts and reason

The concept related solve this problem is the relation between wavelength, frequency, and wave speed.

First, convert the wavelength from millimeters to meters. Then, determine the required frequency by using the relation between the speed of the wave, wavelength, and frequency.

Fundamentals

The relation between the frequency and wavelength is,

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

Here, f is the frequency, $\lambda$ is the wavelength, and v is the speed of the wave.

Convert the value of wavelength from millimeters to meters.

The wavelength is given as,

$\lambda = 1.44{\rm{ mm}}$

Convert the units of wavelength.

$\begin{array}{c}\\\lambda = 1.44{\rm{ mm}}\left( {\frac{{1{\rm{ m}}}}{{{{10}^3}{\rm{ mm}}}}} \right)\\\\ = 1.44 \times {10^{ - 3}}{\rm{ m}}\\\end{array}$

Calculate the required frequency.

The frequency of the wave is given as,

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

Here, v is the speed of the wave and $\lambda$ is the wavelength of the wave.

Substitute $1809{\rm{ m/s}}$ for v and $1.44 \times {10^{ - 3}}{\rm{ m}}$ for $\lambda$ in the above equation.

$\begin{array}{c}\\f = \frac{{1809{\rm{ m/s}}}}{{1.44 \times {{10}^{ - 3}}{\rm{ m}}}}\\\\ = 1.26 \times {10^6}{\rm{ Hz}}\\\end{array}$

Ans:

The required frequency of the wave is $1.26 \times {10^6}{\rm{ Hz}}$.