Question:
A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is :-
A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is :-
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For a string fixed at both ends, \(f_n=nf_1\) and \(L=n\lambda_n/2\); the driving frequency is the third harmonic.
Updated On: Nov 5, 2026
- 180m/s, 80 Hz
- 180m/s, 120 Hz
- 320m/s, 120 Hz
- 320m/s, 80 Hz
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The Correct Option is D
Solution and Explanation
Third harmonic: \(f_3=3f_1=240\) Hz \(\Rightarrow\) fundamental \(f_1=80\) Hz.
For n = 3 loops: \(L=\dfrac{3\lambda}{2}\) \(\Rightarrow\) \(\lambda=\dfrac{2L}{3}=\dfrac{2\times2.0}{3}=\dfrac43\) m.
Speed \(v=f_3\lambda=240\times\dfrac43=320\) m/s.
Answer: (4) 320m/s, 80 Hz
For n = 3 loops: \(L=\dfrac{3\lambda}{2}\) \(\Rightarrow\) \(\lambda=\dfrac{2L}{3}=\dfrac{2\times2.0}{3}=\dfrac43\) m.
Speed \(v=f_3\lambda=240\times\dfrac43=320\) m/s.
Answer: (4) 320m/s, 80 Hz
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