The speed of sound in air is 340 m/s.The shortest air column, closed at one end, which will resonate to a 512 Hz tuning fork is approximately:
A)4.2 cm
B)8.3 cm
C)17 cm
D)33 cm
E)66 cm

Question

Quizplus · Accepted Answer

The resonant frequency of a closed-end air column (with one end closed and the other open) is given by the equation:

f = (n*v)/(4*L)

where:
- f is the resonant frequency (in Hz)
- n is the harmonic number (1 for the fundamental frequency, 2 for the first overtone, 3 for the second overtone, etc.)
- v is the speed of sound in air (340 m/s)
- L is the length of the air column (in meters)

We want to find the length of the air column for the fundamental frequency (n=1) at 512 Hz. Rearranging the formula, we get:

L = (n*v)/(4*f)

L = (1*340)/(4*512)

L = 0.1669921875 m = 16.7 cm

However, this formula gives the length of a full wavelength, which means the actual length of the air column must be half of this value, since a closed-end air column reflects sound waves inverting them, creating a node at the closed end and an antinode at the open end. Therefore, the actual length of the air column is:

L = 16.7/2 = 8.3 cm

So the answer is choice C (17 cm is approximately twice as long as the correct answer, and 4.2 cm and 33 cm are both more than four times too short or too long, respectively).

The Speed of Sound in Air Is 340 M/s