AP Physics 1 Exam Question - Sound Waves

A 440 Hz tuning fork is struck and held over the opening of a pipe. The temperature of the air inside the pipe is 20 °C. The pipe is closed at one end and open at the other. The speed of sound in air at 20 °C is approximately 343 m/s.

a) What is the fundamental frequency of the pipe? b) If the length of the pipe is 0.5 meters, what are the other possible resonant frequencies for the pipe?

Answer:

a) The fundamental frequency of a pipe that is closed at one end and open at the other can be calculated using the formula:

f₀ = (v/2L)

where f₀ is the fundamental frequency, v is the speed of sound in air, and L is the length of the pipe.

Substituting the given values:

f₀ = (343 m/s) / (2 * 0.5 m) = 343 Hz

Therefore, the fundamental frequency of the pipe is 343 Hz.

b) The resonant frequencies of a pipe that is closed at one end and open at the other can be calculated using the formula:

fn = n * f₀

where fn is the nth resonant frequency, n is an integer, and f₀ is the fundamental frequency.

Substituting the values:

For n = 2:

f₂ = 2 * 343 Hz = 686 Hz

For n = 3:

f₃ = 3 * 343 Hz = 1029 Hz

For n = 4:

f₄ = 4 * 343 Hz = 1372 Hz

And so on.

Therefore, the other possible resonant frequencies for the pipe with a length of 0.5 meters are 686 Hz, 1029 Hz, 1372 Hz, and so on.

Note: It is important to consider that the length of the pipe may limit the number of possible resonant frequencies.