# Wavelength, resonance

1. May 3, 2010

### crosbykins

1. The problem statement, all variables and given/known data

-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.

2. Relevant equations
1st harmonic: lambda = 4 * L
3rd harmonic: lambda = 4/3 * L

3. The attempt at a solution
ok so the 3rd resonant legth = .75m
so .75m = 4/3 *L
L = .56m

so for the 1st resonant lenght -> 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!

2. May 3, 2010

### 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?

Last edited: May 3, 2010
3. May 3, 2010

### crosbykins

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

4. May 3, 2010

### crosbykins

ohhh, resonant lenght is simply the length of the air column/pipe...on my test today for some reason i thought resonant lenght 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.