Question

Two cars A and B move in the same direction at constant velocities 18 m/s and 12 m/s respectively, with A behind B. If the drivers of both cars use their
horn (both emitting a frequency 406 Hz) at the same time the beat frequency heard by the driver in Ais
Hz
(Speed of sound in air = 336 m/s)
​

Answer 1

Given:

Two cars A and B move in the same direction at constant velocities 18 m/s and 12 m/s respectively, with A behind B. The drivers of both cars use their horn (both emitting a frequency 406 Hz) at the same time.

To find:

Beat frequency heard by car A driver.

Calculation:

First , let's calculate the apparent frequency heard by car A driver from the sound of car B :

• Car A is observer and Car B is source.

Applying Doppler's Equation:

$\therefore \: f2 = \bigg(\dfrac{v + v_{0} }{v + v_{s}} \bigg) \times f$

$\implies \: f2 = \bigg(\dfrac{336 + 18 }{336 + 12} \bigg) \times 406$

$\implies \: f2 = \bigg(\dfrac{354}{348} \bigg) \times 406$

$\implies \: f2 = 413 \: hz$

So, beat frequency will be :

$\therefore \: \nu = f2 - f1$

$\implies \: \nu =413 - 406$

$\implies \: \nu =7 \: hz$

So, beat frequency will be 7 Hz.