An organ pipe is open at both ends. The frequency of the fourth mode is 316 Hz higher than the frequency of the third mode. If the speed of sound is 340 m/s, then what is the length of the organ pipe?
A) 53.8 cm
B) 59.8 cm
C) 60.3 cm
D) 62.8 cm
E) 64.7 cm

Question

Quizplus · Accepted Answer

The frequency of the fourth mode is given by f4 = (4/2) * (v/2L) = 2v/L, and the frequency of the third mode is given by f3 = (3/2) * (v/2L) = 3v/2L. Therefore, f4 - f3 = v/L = 316 Hz. Solving for L, we get L = v/f4 - f3 = 340 m/s / 316 Hz = 1.076 m = 107.6 cm. Since the organ pipe is open at both ends, its length is half of the wavelength of the fourth mode, so L = 107.6 cm / 2 = 53.8 cm.

An Organ Pipe Is Open at Both Ends