An organ pipe is open at both ends. The frequency of the third mode is 320 Hz higher than the frequency of the second mode. If the speed of sound is 345 m/s, then what is the length of the organ pipe?
A) 64.0 cm
B) 62.6 cm
C) 57.9 cm
D) 53.9 cm
E) 50.3 cm

Question

Quizplus · Accepted Answer

Let L be the length of the organ pipe.

In the second mode, the wavelength of the sound wave is twice the length of the pipe:

λ2 = 2L

In the third mode, the wavelength is (4/3) times the length of the pipe:

λ3 = (4/3)L

Since the speed of sound is given by v = fλ, we can write:

v = f2(2L) and v = f3((4/3)L)

Setting these equations equal to each other and solving for L, we get:

f3 - f2 = v/L * (3/4)

320 = (345 m/s) / L * (3/4)

L = (345 m/s) / (320/0.75) = 0.539 m = 53.9 cm

Therefore, the correct answer is D.

An Organ Pipe Is Open at Both Ends