Imagine siren emitting a sound of frequency $1000\ \mathrm{Hz}$ moves away from you toward a cliff at a…
Imagine siren emitting a sound of frequency $1000\ \mathrm{Hz}$ moves away from you toward a cliff at a speed of $10\ \mathrm{ms}^{-1}$. (i) What is the frequency of the sound you hear coming directly from the siren? (ii) What is the frequency of the sound you hear reflected off from the cliff ? (iii) What beat frequency would you hear? Take the speed of sound in air as $330\ \mathrm{ms}^{-1}$
Solution
Sol. The given situation is shown below.
O • S → | ← S′
Cliff
(i) Frequency of sound reaching directly to us (by S),
$f_1 = \left(\frac{v}{v+v_s}\right) f = \left(\frac{330}{330+10}\right) (1000)$
$= 970.6\ \text{Hz}$
(ii) Frequency of sound which is reflected off from the cliff (from S'),
$f_2 = \left(\frac{v}{v-v_s}\right) f = \left(\frac{330}{330-10}\right) (1000)$
$= 1031.3\ \text{Hz}$
(iii) Beat frequency = $f_2 - f_1 = 60.7\ \text{Hz}$
Answer: 60.7 Hz