Question

An organ pipe of length L open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz. What should be the length of pipe closed at one end, so that its also vibrates in its first harmonic with the same tuning fork?

Answer 1

Let us consider the following diagram organ is open at both ends,

For first harmonic-

L = \(\frac{λ}{2}\)

or λ = 2L

[As, λ= \(\frac{c}{v}\), c = speed of sound air]

\(\frac{c}{v}\)= 2L

or v = \(\frac{c}{2L}\)

For pipe closed at one end-

\(v_1=\frac{c}{4L_1}\)

But v= v₁ [for resonance same tuning fort]

\(\frac{c}{2L}=\frac{c}{4L_1}\) [∴ Speed remains constant]

\(\frac {L_1}{L}=\frac{2}{4}=\frac{1}{2}\)

or L₁ = \(\frac{L}{2}\)