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MHT CET · Physics · Waves and Sound

The pipe open at both ends and pipe closed at one end have same length and both are vibrating in fundamental mode. Air column vibrating in open pipe has resonance frequency \(n_1\) and air column vibrating in closed pipe has resonance frequency \(\mathrm{n}_2\), then

  1. A \(\mathrm{n}_1=2 \mathrm{n}_2\)
  2. B \(\mathrm{n}_1=\mathrm{n}_2\)
  3. C \(2 \mathrm{n}_1=\mathrm{n}_2\)
  4. D \(3 \mathrm{n}_1=4 \mathrm{n}_2\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\mathrm{n}_1=2 \mathrm{n}_2\)

Step-by-step Solution

Detailed explanation

Resonant frequency in open pipe, \(\mathrm{n}_1=\frac{\mathrm{V}}{2 \mathrm{~L}}\)
Resonant frequency in closed pipe, \(\mathrm{n}_2=\frac{\mathrm{V}}{4 \mathrm{~L}}\)
\(\begin{array}{rlrl}
& \therefore & \mathrm{n}_2 & =\frac{\mathrm{V}}{2 \times 2 \mathrm{~L}} \\
& \mathrm{n}_2 & =\frac{\mathrm{n}_1}{2} \\
& \therefore & \mathrm{n}_1 & =2 \mathrm{n}_2
\end{array}\)