Question

Organ pipe a, with both ends open, has a fundamental frequency of 340 hz. the third harmonic of organ pipe b, with one end open, has the same frequency as the second harmonic of pipe

a. how long are (a) pipe a and (b) pipe b? (take the speed of sound to be 343 m/s.)

Answer 1

The fundamental frequency of the open pipe A
Length 'L₀' is, f₀ = U/2L₀ = 340 H₂
the speed of sound in air V= 343m/s
∴343/2L₀ = 340 → length L₀ = 343/2 ×340 = 0.5044 = 50.44
The third harmonic of closed pipe 'B' is
F3₀ = 3V/4LC
The second harmonic of open pipe 'A' is
f2₀ = 2V/2L₀
∴ 3V/4LC = 2V/2L →L₀ = 3L₀/4
⇒ The length of closed pipe B is
Lc = 37.83cm