Question

An ultrasonic scanner is used in a hospital to detect tumours in tissue. The working frequency of the scanner is 4.2 mega Hz. The velocity of sound in the tissue is $1.7km{s}^{-1}$. The wavelength of sound in the tissue is nearest to

• A. $4\times {10}^{-3}$ m
• B. $8\times {10}^{-3}$ m
• C. $4\times {10}^{-4}$ m
• D. $8\times {10}^{-4}$ m

Answer 1

Answer: (C)

$4\times {10}^{-4}$ m

Let,

The working frequency of the scanner is $\nu =4.2MHz=4.2\times {10}^{6}Hz$.

The velocity of sound in the tissue is $v=1.7km{s}^{-1}=1.7\times {10}^{3}m{s}^{-1}$

the wavelength of sound is given by

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

$\lambda =\frac{1.7\times {10}^3}{4.2\times {10}^6}$

$\lambda =0.404\times {10}^{-3}$

$\lambda \approx 4\times {10}^{-4}m$