Question

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

Answer 1

Step 1: Given

Frequency: $f=4.5MHz=4.5\times {10}^{6}Hz$

Speed of sound in air: $v_a=340m/s$

Speed of sound in tissue: $v_t=1.5km/s=1.5\times {10}^{3}m/s$

Step 2: Formula Used

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

Step 3: Calculate the wavelength in air using the formula

$$\begin{gathered} {\lambda }_a=\frac{v_a}{f} \\ =\frac{340m/s}{4.5\times {10}^{6}Hz} \\ =7.6\times {10}^{-5}m \end{gathered}$$

Step 4: Calculate the wavelength in tissue using the formula

$$\begin{gathered} {\lambda }_t=\frac{v_t}{f} \\ =\frac{1.5\times {10}^{3}m/s}{4.5\times {10}^{6}Hz} \\ =3.3\times {10}^{-4}m \end{gathered}$$

Hence, the wavelength in air is $7.6\times {10}^{-5}m$ and in tissue is $3.3\times {10}^{-4}m$.