Question:
Three tuning forks A, B and C have respective frequencies \(n_{1}\), \(n_{2}\) and \(n_{3}\) related as \(n_{1}=1.04n_{2}\) and \(n_{3}=0.99n_{2}\). When A and C are sounded together 5 beats are heard per second. The frequencies of fork A, B and C are respectively.
Three tuning forks A, B and C have respective frequencies \(n_{1}\), \(n_{2}\) and \(n_{3}\) related as \(n_{1}=1.04n_{2}\) and \(n_{3}=0.99n_{2}\). When A and C are sounded together 5 beats are heard per second. The frequencies of fork A, B and C are respectively.
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Use the beat frequency between A and C to get the frequency of B, then the others.
Updated On: Nov 12, 2026
- 99 Hz, 100 Hz, 104 Hz
- 104 Hz, 99 Hz, 100 Hz
- 100 Hz, 104 Hz, 99 Hz
- 104 Hz, 100 Hz, 99 Hz
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
The beat frequency equals the difference of the two frequencies sounded together.
Step 2: Use A and C
\(n_1-n_3=1.04n_2-0.99n_2=0.05n_2=5\), so \(n_2=100\text{ Hz}\).
Step 3: Other frequencies
\(n_1=1.04\times100=104\text{ Hz}\) and \(n_3=0.99\times100=99\text{ Hz}\).
Step 4: Check
\(104-99=5\) beats per second, as given.
Final Answer:
The frequencies of A, B and C are 104 Hz, 100 Hz and 99 Hz. \[ \boxed{\text{(D) }\text{104 Hz, 100 Hz, 99 Hz}} \]
The beat frequency equals the difference of the two frequencies sounded together.
Step 2: Use A and C
\(n_1-n_3=1.04n_2-0.99n_2=0.05n_2=5\), so \(n_2=100\text{ Hz}\).
Step 3: Other frequencies
\(n_1=1.04\times100=104\text{ Hz}\) and \(n_3=0.99\times100=99\text{ Hz}\).
Step 4: Check
\(104-99=5\) beats per second, as given.
Final Answer:
The frequencies of A, B and C are 104 Hz, 100 Hz and 99 Hz. \[ \boxed{\text{(D) }\text{104 Hz, 100 Hz, 99 Hz}} \]
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