A bat emitting an ultrasonic wave of frequency 2 × 10$^{4}$ flies at a speed of 6 m/s between two parallel…
A bat emitting an ultrasonic wave of frequency 2 × 10$^{4}$ flies at a speed of 6 m/s between two parallel walls. Find the two frequencies heard by the bat and the beat frequency between the two. The speed of sound is 330 m/s)
Solution
Sol. Frequency received by bat after reflection from wall (1),
$f_1 = f\left(\frac{v+u}{v-u}\right) = (2 \times 10^4)\left(\frac{330+6}{330-6}\right)$
$= 2.03 \times 10^4\ \mathrm{Hz}$
Frequency received by bat after reflection from wall (2),
$f_2 = f\left(\frac{v-u}{v+u}\right) = (2 \times 10^4)\left(\frac{330-6}{330+6}\right)$
$= 1.9 \times 10^4\ \mathrm{Hz}$
Beat frequency = $f_1 - f_2 = 2.03 \times 10^4 - 1.9 \times 10^4 = 1300\ \mathrm{Hz}$
Answer: 1300 Hz