Question:
Two sound waves having wavelengths 5.0 m and 5.5 m respectively produce 10 beats per second when propagating in a gas. The velocity of sound in the gas is:
Two sound waves having wavelengths 5.0 m and 5.5 m respectively produce 10 beats per second when propagating in a gas. The velocity of sound in the gas is:
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Always convert beat problems into frequency difference using \( f = v/\lambda \) before solving.
Updated On: Jun 10, 2026
- 330 ms\(^{-1}\)
- 550 ms\(^{-1}\)
- 1100 ms\(^{-1}\)
- 220 ms\(^{-1}\)
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The Correct Option is B
Solution and Explanation
Concept:
Beat frequency:
\[
b = |f_1 - f_2|
\]
Wave relation:
\[
f = \frac{v}{\lambda}
\]
Step 1: Write frequencies \[ f_1 = \frac{v}{5.0}, \quad f_2 = \frac{v}{5.5} \]
Step 2: Apply beat condition \[ 10 = \left| \frac{v}{5} - \frac{v}{5.5} \right| \] \[ 10 = v \left( \frac{11 - 10}{55} \right) \] \[ 10 = \frac{v}{55} \]
Step 3: Solve \[ v = 550 \text{ m/s} \]
Step 1: Write frequencies \[ f_1 = \frac{v}{5.0}, \quad f_2 = \frac{v}{5.5} \]
Step 2: Apply beat condition \[ 10 = \left| \frac{v}{5} - \frac{v}{5.5} \right| \] \[ 10 = v \left( \frac{11 - 10}{55} \right) \] \[ 10 = \frac{v}{55} \]
Step 3: Solve \[ v = 550 \text{ m/s} \]
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