Find Air Temperature in a 25.3cm Air Column with 1024Hz Frequency

[Obscurities]

Homework Statement

An air column is closed at on end, with a length of 25.3cm, resonates in the first overtone. If the frequency of the sound wave is 1024Hz, find the air tempature inside the column.

Homework Equations

v=f(wavelength)
v= 332 + v/v+-vs

The Attempt at a Solution

 

[Simon Bridge]

Welcome to PF.
What have you tried?
How are you thinking about this?

Have you been able to find the wavelength?
Do you know how the wavelength is related to the frequency?

 

[Obscurities]

I actually have.. plenty.
wavelength is 1/4 the length
so i it is 4(0.253)

 

[Simon Bridge]

How did you determine the 1st overtone has wavelength 4L? Isn't that the wavelength of the fundamental?

Do you know how the wavelength is related to the frequency?

What have you tried? Please provide at least one example - preferably one which you feel best illustrates your understanding of the problem or where you get stuck.

Without this I cannot help you.

 

[Obscurities]

I thought overtone and fundamental were the same...
Wavelength(Frequency)= Velocity
the longer the wavelength the lower the frequency
the shorter the wavelength the higher the frequency?

4L = 1.012m
v= 4L*f
v= (1.012m)(1024Hz)
=1036.28

T= (1036.28-332)/0.6
= 1173.8 C

Which is entirly incorrect ...

 

[Simon Bridge]

I thought overtone and fundamental were the same...

"An overtone is any frequency higher than the fundamental frequency of a sound."
-- http://en.wikipedia.org/wiki/Overtone#Musical_usage_term (also examples that page)
Musical overtones are usually very close to the harmonics - the first overtone is the second harmonic.

How are you computing temperature from speed?
There are several ways. You should use words to tell me what you are doing.
I'd have exploited that the speed of sound in a gas is proportional to the square-root of it's absolute temperature (and a bunch of other stuff like inverse-mean-molecular-weight) and compare this situation with that at 300K. But you may be expected to use some other method.

 

[Obscurities]

Oh, my I must have skipped that.
Thank you for clearing the my question.

So instead of just 4L, it's actually 4L/3 which is the 2nd resonate.
I am using the formula of velocity= 332 + 0.6(t)
I feel so dumb right now.. Thank You.

 

[Simon Bridge]

I was wondering where that 0.6 factor comes from but I've found it elsewhere so you are going to be fine with that.

It is OK to get stuff wrong - in fact, it is unavoidable when you do science.
That bad feeling you get when you mess up? Ignore it - it's rubbish.
Never let feeling dumb stop you from describing your ideas.
http://www.ted.com/talks/kathryn_schulz_on_being_wrong.html