Calculating Speed of Sound with a Resonating Tube

[KatieLynn]

Homework Statement

A 15.7cm long, closed-end tube, filled with air, resonates when exposed to sound waves with a frequency of 550hz. Calculate the speed of sound.

Homework Equations

V=331.4 + 0.6*Temp.C
V=wavelength*frequency
V=d/t

The Attempt at a Solution

I'm thinking I need to use V=331.4 + 0.6*Temp.C to find the velocity, though temperature is not given I think my teacher told me you can assume it is 20 degrees C if temperature is not given. Is that right? However, that doesn't explain why they gave you the length, so maybe that's not the equation I should even use.

 

[rock.freak667]

Well do you know the equation for the wavelength in a closed-end tube?

The first harmonic is given by $\frac{\lambda}{4}=L$

 

[KatieLynn]

mmm I don't think so, I wasn't aware there there was a separate wavelength equation for closed-end tube things. I thought you could use v=wavelength*frequency or velocity= wavelength/T for all of them.

 

[temaire]

No, this is not the equation you should be using. You should be using $$v = f \lambda$$. You can solve for the wavelength by converting the length into metres, and then multiplyin it by four. Then plug in wavelength and frequency into the equation and you will get the speed.

 

[rock.freak667]

mmm I don't think so, I wasn't aware there there was a separate wavelength equation for closed-end tube things. I thought you could use v=wavelength*frequency or velocity= wavelength/T for all of them.

You need to use the one I posted. But research Standing waves in pipes and they will show you how to get the equations.

 

[KatieLynn]

Ohh! I kind of remember him saying something about that now, isn't it like you multiply it by 4 because its 1/4 the of the length of the wave or something? So, anyway, here's what I did...

15.7cm=0.157m
0.157m*4=.628=wavelength

v=(550hz)(.628)
v=345.4m/s

Correct?

 

[rock.freak667]

Yep 1/4 of the wavelength.

Yes that is correct.

 

[KatieLynn]

thank you :)