Question

Two sound waves of wavelengths 99 cm and 100 cm produce 10 beats in a time of \( t \) seconds. If the speed of sound in air is 330 m/s, then the value of \( t \) in seconds is

• A. 12
• B. 9
• C. 6
• D. 3

Hint:

Beat frequency is the difference between two frequencies; time for given beats is beats divided by beat frequency.

Answer 1

The Correct Option is D

Step 1: Calculate frequencies of two sound waves
Frequency \( f = \frac{v}{\lambda} \), where \( v = 330 \, m/s \).
For wavelength \( \lambda_1 = 99\, cm = 0.99\, m \): \[ f_1 = \frac{330}{0.99} = 333.33\, Hz \] For wavelength \( \lambda_2 = 100\, cm = 1.00\, m \): \[ f_2 = \frac{330}{1.00} = 330\, Hz \] Step 2: Calculate beat frequency
\[ f_{beat} = |f_1 - f_2| = |333.33 - 330| = 3.33\, Hz \] Step 3: Calculate time for 10 beats
Number of beats \( n = 10 \) and \( f_{beat} = \frac{n}{t} \)
\[ t = \frac{n}{f_{beat}} = \frac{10}{3.33} = 3\, \mathrm{seconds}. \] Step 4: Conclusion
The time \( t \) is 3 seconds.