How Do You Calculate the Wavelength in a Closed Pipe Resonance Problem?

[crosbykins]

Homework Statement

-a pipe closed at one end resonates with a turning fork at a length of 25cm. The next resonant length is 75cm. The air temperature is 11.6C. What is the wavelength of the sound produced by the turning fork.

Homework Equations

1st harmonic: lambda = 4 * L
3rd harmonic: lambda = 4/3 * L

The Attempt at a Solution

ok so the 3rd resonant legth = .75m
so .75m = 4/3 *L
L = .56m

so for the 1st resonant length -> lambda = 4 * .56m
=2.25m

since the frequency of the turning fork must equal the frequency of the pipe and the speed of sound stays the same that means the pipe and turning fork will have the same wavelength. so the wavelength of the sound produced by the turning fork is 2.25m.

is that correct...? thanks for the help, in advance!

 

[Stonebridge]

The situation is a little different here.
By resonant length, it seems the question is referring to the actual length of pipe that resonates at the frequency of the fork.
So it looks like this

The 1st resonance and the 2nd resonance are the same frequency and wavelength. They take place in 2 different lengths of tube.
Can you see what the wavelength of the sound is now?

 

[crosbykins]

The situation is a little different here.
By resonent length, it seems the question is referring to the actual length of pipe that resonates at the frequency of the fork.
So it looks like this

The 1st resonance and the 2nd resonance are the same frequency and wavelength. They take place in 2 different lengths of tube.
Can you see what the wavelength of the sound is now?

so lambda is 100cm...1m. doesn't resonant length usually refer to the wavelength of the sound, not acutally length or can it refer to either.

 

[crosbykins]

so lambda is 100cm...1m. doesn't resonant length usually refer to the wavelength of the sound, not acutally length or can it refer to either.

ohhh, resonant length is simply the length of the air column/pipe...on my test today for some reason i thought resonant length was the wavelenght. uh, that's really frustrating I probably lost so many marks when I could have easily done the qs. oh well. thanks for the help, though.

 

[rdl]

I can confirm that your solution is correct. The wavelength of the sound produced by the turning fork is 2.25m. This is because the first resonant length is four times the length of the pipe, which is closed at one end. This is known as the fundamental frequency or the first harmonic. The third resonant length would be four-thirds the length of the pipe, which is the third harmonic. The temperature of the air does not affect the wavelength in this case, as the speed of sound remains constant. Good job on solving the problem!