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
Step-by-step 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