Question

Ultrasonic waves of frequency 4.5 MHz are used to detect tumour in soft tissue. The speed of sound in tissue is 1.5 km s⁻¹ and that in air is 340 m s⁻¹. Find the wavelength of this ultrasonic wave in air and in tissue.

Answer 1

(a) Given:
Frequency of ultrasonic wave f = 4.5 MHz = 4.5 × 10⁶ Hz
Velocity of air v = 340 m/s
Speed of sound in tissue = 1.5 km/s
Wavelength λ = ?
As we know, $v=f\lambda$.
$$\begin{gathered} \therefore \lambda =\frac{340}{4.5\times {10}^6} \\ \Rightarrow \lambda =7.6\times {10}^{-5}\mathrm{m} \end{gathered}$$

(b) Velocity of sound in tissue v_tissue= 1500 m/s
$$\begin{gathered} \lambda =\frac{v_{tissue}}{f} \\ \Rightarrow \lambda =\frac{1500}{4.5\times {10}^{-6}}\mathrm{m} \\ \Rightarrow \lambda =3.3\times {10}^{-4}\mathrm{m} \end{gathered}$$