Please help me!

Question

You are building a pipe organ with open-tube pipes spanning the range of human hearing (20. Hz to 20. kHz), 

a) What would be the length of the shortest pipe? 

b) What would be the length of the longest pipe?

Answer 1

The speed of sound in air at room temperature = 340m/s

The length of a pipe required to produce a particular pitch is determined by the speed of sound in air and the frequency of the pitch.

In order to calculate the length of shortest pipe required to produce a frequency of 20Hz, Using the formula,  = v/f = 340/20 = 17.15m

For a pipe open at both ends the fundamental resonance frequency will have a velocity maximum at both ends with a velocity null at the midpoint, so the length of pipe is one half wavelength. Length = ½ x  wavelength = ½ x 17.15 = 8.58m

In order to calculate the length of longest pipe required to produce a frequency of 20kHz, Using the formula,  = v/f = 340/20000 = 0.01715 m

For a pipe open at both ends the fundamental resonance frequency will have a velocity maximum at both ends with a velocity null at the midpoint, so the length of pipe is one half wavelength. Length = ½ x  wavelength = ½ x 0.01715 = 0.00858m