Question

A motor-cyclist moving towards a huge cliff with a speed of 18 km/h, blows a horn of source frequency 325 Hz. If the speed of the sound in air is 330 m/s, the number of beats heard by him is

• A. 5
• B. 4
• C. 7
• D. 6

Answer 1

The Correct Option is A

The phenomenon of beats occurs when two sounds of slightly different frequencies combine.
The number of beats is the absolute difference between the frequencies of the two sounds: the source frequency and the observed frequency. 

To calculate the observed frequency \(f_o \) when the source is moving towards the observer, we use the Doppler effect formula:
\(f_o = f_s \left( \frac{v}{v - v_s} \right) \)
 where: - \(f_o \) is the observed frequency, 
- \(f_s = 325 \text{Hz} \) is the source frequency, 
-\(v = 330 \text{m/s} \) is the speed of sound in air, 
- \(v_s = 5 \text{m/s} \)  is the speed of the source (since the motorcyclist is moving towards the cliff, the speed of the source relative to the observer is 5 m/s). 

Substituting these values into the formula:
\(f_o = 325 \times \frac{330}{325} = 330 \text{Hz}\)
 The number of beats is the difference between the observed frequency \(f_o \) and the source frequency \(f_s \):\(\Delta f = |f_o - f_s| = |330 - 325| = 5 \text{beats}\)