Question

Diagnostic ultrasound of frequency 4.50 MHz is used to examine tumors in soft tissue. (a) What is the wavelength in air of such a sound wave? (b) If the speed of sound in tissue is 1500 m/s, what is the wavelength of this wave in tissue?

Answer 1

(a) $7.62 \times 10^{-5} m$ is the wavelength in air of such a sound wave.

(b) $3.33 \times 10^{-4}\ m$ is the wavelength of this wave in tissue.

Explanation:

Frequency and wavelength can be related by the equation,

              Velocity = Wavelength x Frequency

              $v=\lambda \times f$

where,

v - velocity of light for all EM (electromagnetic) waves in vacuum

Given:

f - 4.50 MHz = $4.50 \times 10^{6} \mathrm{Hz}$

a) To find the wavelength in air

We know,

Speed of sound in air = 343 m/s

Apply given frequency and speed of sound in air, we get

        $\lambda=\frac{v}{f}=\frac{343}{4.5 \times 10^{6}}=76.2 \times 10^{-6}=7.62 \times 10^{-5}\ \mathrm{m}$

b) If the speed of sound in tissue is 1500 m/s, find the wavelength of this wave in tissue

Speed of sound in tissue, v = 1500 m/s

        $\lambda=\frac{v}{f}=\frac{1500}{4.5 \times 10^{6}}=333.33 \times 10^{-6}=3.33 \times 10^{-4} \mathrm{m}$