Consider two pipes of the same length. One pipe is open at both ends and the other pipe is closed on one end but open at the other end.

If the fundamental frequency of the totally open pipe is 300 Hz, what is the fundamental frequency of the other pipe?

a. 150 Hz

b. 300 Hz

c. 450 Hz

d. 600 Hz

The correct option is a. 150 Hz

Explanation:

For an open pipe,

f₀₁ = v/2l ... Equation 1

for a closed pipe,

f₀₂ = v/4l ... Equation 2

Where l = length of the pipe (length of both pipes are equal), v = speed of sound in air, f₀₁ = fundamental frequency of the opened pipe, f₀₂ = fundamental frequency of the closed pipe

Dividing Equation 1 by Equation 2,

f₀₁/f₀₂ = v/2l/v/4l

f₀₁/f₀₂ = 4lv/2lv

f₀₁/f₀₂ = 2 ... Equation 3

Given: f₀₁ = 300 Hz

Substituting this value into equation 3

300/f₀₂ = 2

making f₀₂ the subject of the equation,

f₀₂ = 300/2

f₀₂ = 150 Hz

The correct option is a. 150 Hz