Standing sound waves: A tube open at one end and closed at the other end produces sound having a fundamental frequency of 350 Hz. If you now open the closed end, the fundamental frequency becomes
A) 87.5 Hz.
B) 175 Hz.
C) 350 Hz.
D) 700 Hz.
E) 1400 Hz.

Question

Quizplus · Accepted Answer

When a tube is closed at one end, the fundamental frequency is given by f = v/4l, where f is the frequency, v is the speed of sound, and l is the length of the tube. When the tube is open at both ends, the fundamental frequency is given by f = v/2l. When the closed end is opened, the effective length of the tube is halved, so the new fundamental frequency is twice the old one, or 700 Hz. Alternatively, we can consider that the closed end of the tube forms a node for the standing wave, while the open end forms an antinode. When the closed end is opened, the node moves to the new open end, which effectively doubles the length of the tube and halves the frequency of the standing wave, giving a new fundamental frequency of 175 Hz.

Standing Sound Waves: a Tube Open at One End and Closed