Question:
Two identical piano wires, when tuned to a fundamental frequency of 400 Hz, produce no beats. One wire is then slightly tightened, and the beat frequency heard is 2 Hz. What is the new fundamental frequency of the tightened wire?
Two identical piano wires, when tuned to a fundamental frequency of 400 Hz, produce no beats. One wire is then slightly tightened, and the beat frequency heard is 2 Hz. What is the new fundamental frequency of the tightened wire?
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Tighten = Frequency Up. Loosen = Frequency Down.
Updated On: May 5, 2026
- 398 Hz
- 402 Hz
- 404 Hz
- 396 Hz
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Concept
The frequency of a stretched string $n$ is directly proportional to the square root of its tension ($n \propto \sqrt{T}$).
Step 2: Meaning
Tightening a wire increases its tension, which necessarily increases its frequency.
Step 3: Analysis
Beat frequency is the difference between two frequencies ($|n_1 - n_2| = 2$ Hz). Since the wire was tightened, the new frequency must be $400 + 2 = 402$ Hz.
Step 4: Conclusion
The new fundamental frequency is 402 Hz.
Final Answer: (B)
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