Q4E - University Physics with Modern Physics

Question

15.4. BIO Ultrasound Imaging. Sound having frequencies above the range of human hearing (about 20,000 Hz) is called ultrasound. Waves above this frequency can be used to penetrate the body and to produce images by reflecting from surfaces. In a typical ultrasound scan, the waves travel through body tissue with a speed of 1500 m/s . For a good, detailed image, the wavelength should be no more than 1.0 mm. What frequency sound is required for a good scan?

Step-by-Step Solution

Answer

The frequency of sound wave is $1.5\times {10}^{-6} \mathrm{Hz}$ _.

STEP 1:The frequency of sound wave concept.

The quantity of waves passing through a fixed place in a unit of time is referred to as frequency.

 

The frequency of the wave is given by 

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

Here, $\mathrm{\lambda }$ is the wavelength of the wave, v is the speed of sound., f is the frequency of wave.

Step 2: To calculate the frequency of the sound wave

Consider the given data as below.

The velocity, $\mathrm{v}=1500 \mathrm{m}/\mathrm{s}$ 

The wavelength, $\mathrm{\lambda }=1.0 \mathrm{mm}$ 

 

The ultrasound waves travel with a speed of 1500 m/s to scan the body with a wavelength of around 1.0mm, Frequency of the sound wave is given by 

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

 

Substitute 1500m/s for v and 1.0mm for $\mathrm{\lambda }$ in the above equation.

 

_{$$\begin{gathered} \mathrm{f}=\frac{\mathrm{v}}{\mathrm{\lambda }} \\ =\frac{1500 \mathrm{m}/\mathrm{s}}{1.0 \mathrm{mm}} \\ =\frac{1500 \mathrm{m}/\mathrm{s}}{\left(1.0 \mathrm{mm}\right)\left({\displaystyle \frac{{10}^{-3} \mathrm{m}}{1\mathrm{mm}}}\right)} \\ =1.5\times {10}^{-6} \mathrm{Hz} \end{gathered}$$} 

 

Therefore, the frequency of sound wave is $1.5\times {10}^{-6} \mathrm{Hz}$.