Question:
The fundamental frequency of a sonometer wire is 50 Hz for some length and tension. If the length is increased by 25% by keeping tension same, then frequency change of second harmonic is
The fundamental frequency of a sonometer wire is 50 Hz for some length and tension. If the length is increased by 25% by keeping tension same, then frequency change of second harmonic is
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For a stretched string, frequency is inversely proportional to length when tension is constant.
Updated On: Feb 18, 2026
- decreased by 10%
- decreased by 20%
- decreased by 5%
- decreased by 15%
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The Correct Option is B
Solution and Explanation
Step 1: Frequency relation for a stretched string.
For a sonometer wire, frequency is given by \[ f \propto \frac{1}{L}, \] when tension and linear density remain constant.
Step 2: Effect of increase in length.
If length is increased by 25%, then \[ L' = 1.25L. \] Hence, new frequency becomes \[ f' = \frac{f}{1.25} = 0.8f. \]
Step 3: Change in second harmonic frequency.
Second harmonic frequency is directly proportional to the fundamental frequency. Therefore, it also becomes 80% of its original value.
Step 4: Conclusion.
The frequency decreases by 20%.
For a sonometer wire, frequency is given by \[ f \propto \frac{1}{L}, \] when tension and linear density remain constant.
Step 2: Effect of increase in length.
If length is increased by 25%, then \[ L' = 1.25L. \] Hence, new frequency becomes \[ f' = \frac{f}{1.25} = 0.8f. \]
Step 3: Change in second harmonic frequency.
Second harmonic frequency is directly proportional to the fundamental frequency. Therefore, it also becomes 80% of its original value.
Step 4: Conclusion.
The frequency decreases by 20%.
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