Question:
Two waves of wavelengths 50 cm and 51 cm produce 12 beats per second. The velocity of sound is:
Two waves of wavelengths 50 cm and 51 cm produce 12 beats per second. The velocity of sound is:
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Beat frequency is the absolute difference between two wave frequencies.
Updated On: Oct 6, 2026
- $306~ms^{-1}$
- $331~ms^{-1}$
- $340~ms^{-1}$
- $360~ms^{-1}$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
The frequency $f = v/\lambda$. The beat frequency is $f_1 - f_2 = 12$.
Step 2: Meaning
$v/0.50 - v/0.51 = 12$.
Step 3: Analysis
$v(2 - 1/0.51) = 12 \implies v(2 - 1.96078) = 12 \implies v(0.039215) = 12$. $v = 12 / 0.039215 = 306~ms^{-1}$.
Step 4: Conclusion
The velocity of sound is $306~ms^{-1}$.
Final Answer: (A)
The frequency $f = v/\lambda$. The beat frequency is $f_1 - f_2 = 12$.
Step 2: Meaning
$v/0.50 - v/0.51 = 12$.
Step 3: Analysis
$v(2 - 1/0.51) = 12 \implies v(2 - 1.96078) = 12 \implies v(0.039215) = 12$. $v = 12 / 0.039215 = 306~ms^{-1}$.
Step 4: Conclusion
The velocity of sound is $306~ms^{-1}$.
Final Answer: (A)
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