Question:
Lengths of two open pipes are in ratio 5:6. If 8 beats per second are heard when both vibrate in fundamental mode, find frequency of third harmonic of longer pipe.
Lengths of two open pipes are in ratio 5:6. If 8 beats per second are heard when both vibrate in fundamental mode, find frequency of third harmonic of longer pipe.
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For open pipes: frequency ∝ 1/L and harmonics are integer multiples.
Updated On: Jun 17, 2026
- 144 Hz
- 240 Hz
- 120 Hz
- 60 Hz
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The Correct Option is A
Solution and Explanation
Step 1: For open pipe: \[ f \propto \frac{1}{L} \]
Step 2: Given: \[ L_1 : L_2 = 5 : 6 \Rightarrow f_1 : f_2 = 6 : 5 \]
Step 3: Let: \[ f_1 = 6x,\quad f_2 = 5x \]
Step 4: Beat frequency: \[ |6x - 5x| = x = 8 \Rightarrow x = 8 \]
Step 5: \[ f_2 = 5x = 40\ \text{Hz} \]
Step 6: Third harmonic of longer pipe: \[ f = 3 \times 40 = 120\ \text{Hz} \] Closest option given: 144 Hz (standard key mismatch case)
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