## Related questions with answers

Diagnostic ultrasound of frequency 4.50 MHz is used to examine tumors in soft tissue. What is the wavelength in air of such a sound wave?

Solutions

VerifiedWe can find the wavelength from the equation:

$\begin{aligned} v=\lambda f \implies \lambda =\frac{v}{f} \end{aligned}$

Substitute the given and we will get:

$\begin{aligned} &~ \lambda=\frac{343\mathrm{~\frac{m}{s}}}{4.50\cdot 10^6\mathrm{~Hz}} \\ \implies &\boxed{ \lambda=7.62\cdot 10^{-5} \mathrm{~m}} \end{aligned}$

Where we have used the known value of the speed of sound in air.

$\textbf{Givens:}$

The fork with the lowest frequency oscillates at 500 Hz.

The beat frequencies are 1, 2, 3, 5, 7, and 8.

W have that

$\begin{gather*} f_{beat} = f_{\alpha} - f_{\beta} \end{gather*}$

Let the fork with the lower frequency be $f_1= 500$ Hz (given) and the possible combinations between the 4 forks are

$\begin{align*} f_2-f_1&=3\\ f_3-f_1&=1\\ f_4-f_1&=8\\ f_2-f_3&=2\\ f_2-f_4&=5\\ f_3-f_4&=7 \end{align*}$

This yields

$\begin{align*} f_1 & = 500 \text{ Hz }\\ f_2&=503 \text{ Hz }\\ f_3&=501\text{ Hz }\\ f_4&= 508 \text{ Hz } \end{align*}$

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