COMEDK · Physics · 16. Waves and Sound
The fundamental frequency of sound produced in an open pipe of length \(\mathrm{L}_1\) is same as the frequency of the \(3^{\text {rd }}\) harmonic of the sound produced in the closed pipe of length \(\mathrm{L}_{\mathrm{2}}\) Then the ratio of \(\dfrac{\boldsymbol{L}_{\mathrm{1}}}{\boldsymbol{L}_{\mathrm{2}}}\) is :
- A \(\dfrac{L_1}{L_2}=\dfrac{1}{3}\)
- B \(\dfrac{L_1}{L_2}=\dfrac{2}{3}\)
- C \(\dfrac{L_1}{L_2}=\dfrac{3}{2}\)
- D \(\dfrac{L_1}{L_2}=\dfrac{3}{1}\)
Answer & Solution
Correct Answer
(B) \(\dfrac{L_1}{L_2}=\dfrac{2}{3}\)
Step-by-step Solution
Detailed explanation
The fundamental frequency of an open pipe of length \(L_1\) is given by \(f_1 = \dfrac{v}{2L_1}\), where \(v\) is the speed of sound. The frequencies of a closed pipe of length \(L_2\) are given by \(f_n = \dfrac{nv}{4L_2}\), where \(n\) is an odd integer (…
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