A small source of sound vibrating at a frequency of 500 Hz is rotated in a circle of radius 100/π cm with a constant angular speed of 5.0 revolutions per second. A listener is situated in the plane of the circle.

Question

Quantrex Academy · Accepted Answer

Correct answer: C. 485 Hz and 515 Hz

The linear speed of the source is given by

v_s = R\omega

.

Given the radius

R = \dfrac{100}{\pi} \text{ cm} = \dfrac{1}{\pi} \text{ m}

and angular speed

\omega = 5.0 \text{ rev/s} = 10\pi \text{ rad/s}

, we get:

v_s = \left(\dfrac{1}{\pi}\right)(10\pi) = 10 \text{ m/s}

The maximum frequency is observed when the source moves directly towards the listener:

f_\max = f_0 \left( \dfrac{v}{v - v_s} \right) = 500 \left( \dfrac{332}{332 - 10} \right) = 500 \left( \dfrac{332}{322} \right) \approx 515.5 \text{ Hz}

The minimum frequency is observed when the source moves directly away from the listener:

f_\min = f_0 \left( \dfrac{v}{v + v_s} \right) = 500 \left( \dfrac{332}{332 + 10} \right) = 500 \left( \dfrac{332}{342} \right) \approx 485.4 \text{ Hz}

The closest values are

485 \text{ Hz}

and

515 \text{ Hz}

.

A small source of sound vibrating at a frequency of 500 Hz is...

Options

Correct answer

Step-by-step solution

More from Sound Waves