A pipe that is open at both ends has a fundamental frequency of 320 Hz when the speed of sound in air is 331 m/s.

Question

(a) What is the length of this pipe?

(b) What are the next two harmonics?

(c) What is the fundamental frequency of this pipe when the speed of sound in air is increased to 370 m/s due to a rise in the temperature of the air?

Answer 1

"Open Pipe" equations needed:

V = f_nw_n

f_n = (nv) / (2L)

w_n = (2L) / (n)

f_n = (n) x (f₀)

Variable Definitions:

V = speed of sound

f_n = frequency of the n^th harmonic

f₀ = fundamental frequency (f₁)

w_n or "lambda" = wavelenght of the n^th harmonic

n = harmonic #

a) 0.517 meters

b) f₂= 640 Hz, f₃=960 Hz

c) 357.83 Hz