Question

In a gas, two waves of wavelengths 1 m and 1.01 m are superposed and produce 10 beats in 3 s. The velocity of sound in the medium is

• A. 300 m/s
• B. 336.7 m/s
• C. 360.2 m/s
• D. 270 m/s

Hint:

Beat frequency \(= |f_1 - f_2| = v\left|\dfrac{1}{\lambda_1} - \dfrac{1}{\lambda_2}\right|\). This helps find speed of sound when two close wavelengths are given.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Beat frequency \(= |f_1 - f_2|\). Using \(f = v/\lambda\): \(f_1 - f_2 = v\left(\dfrac{1}{\lambda_1} - \dfrac{1}{\lambda_2}\right)\).
Step 2: Detailed Explanation:
Beat frequency \(= 10/3\) beats/s \[ \frac{10}{3} = v \left(\frac{1}{1} - \frac{1}{1.01}\right) = v \times \frac{0.01}{1.01} \] \[ v = \frac{10}{3} \times \frac{1.01}{0.01} = \frac{10 \times 101}{3} = \frac{1010}{3} \approx 336.7 \text{ m/s} \]
Step 3: Final Answer:
The velocity of sound is 336.7 m/s.