# Frequency in pipes

1. Apr 10, 2004

### eku_girl83

First of all, thanks to everyone on the physics forum! My semester is almost over and I know I never would have gotten through it without the help of the people on these boards :)
Here's my question:
A certain pipe produces a fundmanetal frequency of 218 Hz in air. If the pipe is filled with helium at the same temperature, what fundamental frequency does it produce? The molar mass of air is 28.8 g/mol and the molar mass of helium is 4 g/mol.
I used v=lamda*f
344=lambda*218
lambda=1.578

Then, I assumed the wavelength (lambda) would be constant. From a table, I found the value of sound in helium to be 927 m/s. So 927=(1.578)f to get f=587.4593 Hz.
This is incorrect. Where did I go wrong? I'm not really what to make of the molar masses.

eku_girl

2. Apr 10, 2004

### harsh

Maybe its just a simple ratio of mass to frequency? Highly doubt it though.

3. Apr 10, 2004

### krab

Somewhere in your notes, you must have the fact that speed of sound is proportional to deinsity to the power -1/2. Take sqrt(28.8/4) multiply by 218 Hz. I get 585 Hz, which is very close to your value.

4. Apr 10, 2004

### enigma

Staff Emeritus
Are you entering the answer into a computerized system?

If so, check your significant figures. I doubt you'll know the frequency down to the 100 microHz.

5. Apr 11, 2004

### eku_girl83

sqrt (28.8/4)^1/2 * 218 still doesn't yield the correct answer. Also, the reason I have so many significant figures in my answer is because we submit our homework to an online program which only permits for a 2% deviation from the published answer.

6. Apr 11, 2004

### eku_girl83

sqrt (28.8/4)^1/2 * 218 still doesn't yield the correct answer. Also, the reason I have so many significant figures in my answer is because we submit our homework to an online program which only permits for a 2% deviation from the published answer.
Does anyone have an idea on how to do this? I checked my notes and my textbook, but I have nothing on the relationshiop between frequency and molar mass. Please help

7. Apr 11, 2004

### Staff: Mentor

I believe that you also have to consider that He is monatomic while air is diatomic. The speed of sound is proportional to sqrt(γ/M), where M is the molar mass and where γ is 3/2 for a (ideal) monatomic gas and 5/2 for a diatomic gas. So Vhelium = sqrt[(3/5)(28.8/4)] Vair = 2.0785 Vair. So I get the frequency in Helium to be about 453 Hz.

8. Apr 12, 2004

### krab

My bad. I forgot about $\gamma$