A vibrating tuning fork of frequency 640 Hz is held above a tube filled with water.Assume the speed of sound to be 330 m/s.As the water level is lowered,consecutive maxima in intensity are observed at intervals of about
A)12.9 cm
B)19.4 cm
C)25.8 cm
D)51.7 cm
E)194 cm

Question

Quizplus · Accepted Answer

The wavelength of sound in the tube is equal to four times the length of the tube when a resonance occurs. Therefore,
λ = 4L

Speed of sound, v = 330 m/s
Frequency of tuning fork, f = 640 Hz

The equation of speed of sound, frequency, and wavelength is given by:
v = fλ

Therefore,
λ = v/f = 330/640 = 0.51562 m

One-fourth of wavelength for the resonance to occur is equal to the length of the air column. Therefore,
L = λ/4 = 0.51562/4 = 0.1289 m = 12.9 cm

Hence, consecutive maxima in intensity are observed at intervals equal to the length of the air column in the tube, which is 12.9 cm. Thus, the correct choice is C.

A Vibrating Tuning Fork of Frequency 640 Hz Is Held