A 30 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 wavelength of the third mode of vibration?
A) 48 cm
B) 36 cm
C) 30 cm
D) 24 cm
E) 12 cm

Question

Quizplus · Accepted Answer

The third mode of vibration in an organ pipe open at one end and closed at the other corresponds to having 5/4 wavelengths fit into the length of the pipe. The fundamental frequency (first mode) corresponds to 1/4 of a wavelength fitting into the pipe. Therefore, for the third mode, the wavelength λ can be found using the length of the pipe (L) as L = (5/4)λ, which gives λ = 4L/5. Substituting L = 30 cm gives λ = (4*30)/5 = 24 cm.

A 30 Cm Long Organ Pipe Is Filled with Air