Question

Calculate the length of a pipe that has a fundamental frequency of 232 Hz. (Take the speed of sound in air to be 343 m/s.)

Answer 1

Complete question:

Calculate the length of a pipe that has a fundamental frequency of 232 Hz. (Take the speed of sound in air to be 343 m/s.)

a) Assume the pipe is closed at one end. m

(b) Assume the pipe is open at both ends. m

Answer:

(a) The length of the pipe if it is closed at one end is 0.37 m

(b) The length of the pipe if it is open at both ends is 0.74 m

Explanation:

Given;

fundamental frequency of the pipe, F₀ = 232 Hz

speed of sound in air, V = 343 m/s

(a) Assuming a closed pipe, the wavelength of the fundamental frequency is given by;

L = λ₀/4

λ₀ = 4L

The relationship between frequency, wavelength and speed is given by;

V = F₀λ₀

substitute the value of λ

V = F₀(4L)

V = 4F₀L

L = V / 4F₀

L = (343) / (4 x 232)

L = 0.37 m

(b) Assuming an open pipe, the wavelength of the fundamental frequency is given by;

L = λ₀/2

λ₀ = 2L

V = F₀λ₀

substitute the value of λ

V = F₀(2L)

V = 2F₀L

L = V / 2F₀

L = (343) / (2 x 232)

L = 0.74 m