A pipe of length 80 cm is open at both ends. A second pipe, closed at one end, has the same fundamental frequency as the open pipe. The length of the second pipe is:

Question

A steel wire with mass per unit length \( 7.0 \times 10^{-3} \, \text{kg/m} \) is under a tension of \( 70 \, \text{N} \). The speed of transverse waves in the wire will be:

Answer 1

Step 1: Open pipe fundamental.
f₁ = v/(2L₁); with L₁ = 80 cm, f₁ = v/160.

Step 2: Closed pipe fundamental.
f₂ = v/(4L₂).

Step 3: Equating frequencies.
v/160 = v/(4L₂).

Step 4: Solving for L₂.
4L₂ = 160 → L₂ = 40 cm.

Step 5: Physical note.
A closed pipe's fundamental is half that of an open pipe of the same acoustic length scale.

Step 6: Conclusion.
The required closed pipe length is 40 cm.

A pipe of length 80 cm is open at both ends. A second pipe, closed at one end, has the same fundamental frequency as the open pipe. The length of the second pipe is:

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The Correct Option is C

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