Pipe A is 0.50 m long and open at both ends. Pipe B is open at one end and closed at the other end. Determine the length of pipe B so that it has the same fundamental frequency as A ...

Answer: length of pipe B = 0.25m

Explanation: pipe A is an open pipe with length 0.50m, the length is related to the wavelength of sound as shown below

L = λ/2 hence λ = 2L

But L = 0.50m, thus λ = 0.50 * 2 = 1m.

But v = fλ, hence f = 350/1 = 350Hz

Assuming the speed of sound in air = 350Hz.

Thus frequency of sound in pipe A is 350Hz

Pipe B is open at one end and closed at the other.

The length of air and wavelength are related by the formulae

L = λ/4

Hence λ = 4L

But v = fλ

f = v/λ but v = 350m/s

f = 350/4L.

Since the frequency of sound in pipe A is the same as pipe B, thus

350 = 350 / 4L.

350 * 4L = 350

1400 * L = 350

L = 350/1400

L = 0.25m