Question

If three sources of sound of frequencies \( (n-1), n, (n+1) \) are vibrated together, the number of beats produced and heard per second respectively are:

• A. 4 and 2
• B. 4 and 4
• C. 2 and 2
• D. 2 and 4

Hint:

The beat frequency is the absolute difference between two frequencies: \( |f_2 - f_1| \).
- When three frequencies are given, find beats between each pair and sum appropriately.

Answer 1

The Correct Option is A

The beat frequency is given by: \[ \text{Beat frequency} = |f_2 - f_1| \] Given frequencies are \( (n-1), n, (n+1) \). 1. Beats between \( n+1 \) and \( n-1 \): \[ |(n+1) - (n-1)| = |n+1 - n +1| = 2 \] 2. Beats between \( n \) and \( (n-1) \): \[ |n - (n-1)| = |n - n +1| = 1 \] 3. Beats between \( n+1 \) and \( n \): \[ |(n+1) - n| = 1 \] 4. Total beats heard per second: \[ 2 + 1 + 1 = 4 \] Thus, the correct answer is \(\boxed{4 \text{ and } 2}\).