Question

A certain pipe has resonant frequencies of 165 Hz, 275 Hz, and 385 Hz, with no other resonant frequencies between these values.

(a) Is this a pipe open at both ends or closed at one end?

(b) What is the fundamental frequency of this pipe?

(c) How long is this pipe? (Use the speed of sound in air at 20°C.)

Answer 1

given

resonant frequencies

165Hz : 275Hz : 385Hz

Resonant frequencies = 385 Hz, 495 Hz, and 605 Hz ,here differences is 110

Fundamental fequency = F = 110/2 = 55 Hz with

First overtone = O1 = 3F = 165 Hz
Second overtone = O2 = 5F = 275 Hz
Third overtone = O3 = 7F = 385 Hz

When you have overtones with harmonics at 3F, 5F and 7F, that is typical of an open pipe.

from the above it is clear that the freqency of pipe is odd multiples of fundamental so the pipe is closed at one end.

b) the first frequency is f₅ = 5f_o

             f₀ = f₅/5 = 165Hz/5 = 33Hz

c) the length of the tube is

L = v/4f₀

= 343m/s/4 * 55HZ = 1.55m