1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fundamental frequencies and temperature

  1. Jan 6, 2007 #1
    1. The problem statement, all variables and given/known data
    The frequency of the note f_4 is f_F.
    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?

    ans= v/(4*f_F), where v is the speed of sound in air.

    Now the part which troubles me:

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

    2. Relevant equations

    (fundamental frequency)=v/4L where L is the length of a closed pipe.
    and

    v=k*sqrt(T) where k is a constant (suitable for this situation, nothing else is known/varying)

    3. The attempt at a solution
    My initial reaction was to say that since the wavelength in the closed pipe must remain the same (4*L) the frequency varies linearly with speed of sound. So for frequency to the divided by four, so must speed, for speed to be divided by four temperature must be divided by 4^2=16, so my answer was T/16. But I'm being told that this is wrong, and that the answer includes the variable "f".

    Any help?
     
  2. jcsd
  3. Jan 6, 2007 #2

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    It is asking for a temperature. I'm not sure what you've done so far but you should start from here;

    [tex]F_{0}=\frac{k\sqrt{T}}{4L}[/tex]
     
  4. Jan 6, 2007 #3
    Hmmmm.... but surely that equation will just return the answer t/16?
     
  5. Jan 6, 2007 #4

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Reread the question. You want to get something of the form of T = ....
     
  6. Jan 6, 2007 #5

    Gokul43201

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I think you're either misunderstanding this part of the question, or not paying close enough attention with the calculation.

    Let me restate the question in a form that might help: If the fundamantal frequency is f_F at temperature T, then at what temperature is the fundamental frequency = f?
     
  7. Jan 6, 2007 #6
    I'm afraid I'm really missing something here. I really cannot see what is wrong with this as a solution:

    [tex]F(x)=\frac{k\sqrt{x}}{4L}[/tex] Where x is the temperature, F is the fundamental frequency.

    For f= [tex]f_F[/tex] we have x = T.

    so [tex]F(T)=\frac{k\sqrt{T}}{4L} = f_F[/tex]

    we want to find y, where F(y)=f. We know that [tex]\frac{f_F}{4} = f[/tex]

    so F(y)=F(T)= [tex]\frac{k\sqrt{y}}{4L} = \frac{k\sqrt{T}}{16L} [/tex]

    Which eventually gives y = T/16. I know it's a bit long winded for what it's actually doing, but I can't see what's wrong with it...
     
  8. Jan 6, 2007 #7

    Gokul43201

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    And how do we know this?
     
  9. Jan 7, 2007 #8
    well I assumed that if f_F was f_4, then it's the fourth harmonic of f, so f_4=4f. Is this an incorrect assumption?
     
  10. Jan 7, 2007 #9
    gah. so it is. that's a bit frustrating... ah well. thanks a lot for the help and time.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Fundamental frequencies and temperature
  1. Fundamental Frequency (Replies: 2)

Loading...