A 25.0 cm long organ pipe is filled with air and is open at one end and closed at the other. The speed of sound in air at 0°C is 331 m/s. What is the frequency of the fourth mode of vibration?
A) 1,550 Hz
B) 1,750 Hz
C) 2,320 Hz
D) 2,720 Hz
E) 3,170 Hz

Question

Quizplus · Accepted Answer

The frequency of a pipe that is open at one end and closed at the other is given by:

fn = (2n - 1)c/4L

where 
n = mode number (1, 2, 3, ...)
c = speed of sound in air
L = length of the pipe

Substituting the given values: 
n = 4
c = 331 m/s
L = 25 cm = 0.25 m

We get:
f4 = (2(4) - 1)c/4L = 9c/4L = 9(331)/(4 x 0.25) = 2328.75 Hz

Rounded to the nearest whole number, the answer is choice C) 2,320 Hz.

A 250 Cm Long Organ Pipe Is Filled with Air and and Is