Temperature and frequency in an organ pipe

[erik-the-red]

Information:

The frequency of the note $${\rm F}_4$$ is $$f_F$$.

1. If an organ pipe is open at one end and closed at the other, what length must it have for its fundamental mode to produce this note at a temperature of T? The speed of sound is $$v_s$$.

I used the equation $$f_n = \frac{nv}{4L}$$. Plugging in known values resulted in $$L = \frac{1}{4}\frac{v_s}{f_F}$$. This is correct.

2. At what air temperature will the frequency be f? (Ignore the change in length of the pipe due to the temperature change.)

I have no idea how to start this.

 

[jmcgraw]

will the frequency be f? What's the value of f?

I know the speed of sound varies at different temperatures. Our book/teacher never gave us a formula though. Velocity of sound is given by v = sqrt(B/rho). Where B is the bulk modulus of air and rho is the density. So if you can figure out how B and rho varie with temperature you should get somewhere.

Maybe someone else can help further...

 

[erik-the-red]

You're right about temperature affecting velocity; my book made explicit mention of that.

But, it, too gave no formula for this type of problem in the respective section.

 

[erik-the-red]

I asked my professor and he gave an equation where frequency is 331 + 0.6T.

I tried this, but was unsuccessful.

How do I get wavelength from this?

 

[Astronuc]

I asked my professor and he gave an equation where frequency is 331 + 0.6T.

That formula is for the speed of sound in air at temperature T, where T is in °C, and speed in m/s.
Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe.html

v = $\lambda$ f, where $\lambda$ is wavelength and f is frequency.

http://hyperphysics.phy-astr.gsu.edu/hbase/wavrel.html#c1