Wave Speed Increases: Freq or Period Increases?

[justadream]

TBR Physics Book II page 42 # 44

This passage is about creating waves in pipes.

"If the temperature of the room changes from 30 to 33, which of the following statements is true"?

Correct Answer: "The pitch of the wave produced in the pipe changes; the pitch of the wave produced by the string does not" (***ignore the second part***)

I understand that as temperature increases, wave speed increases.

But when wave speed increases, how do you know that it is FREQUENCY and not WAVELENGTH that is increasing when the wave speed increases?

I guess I could reason it out using the formulas: f= nv / 2L and Wavelength = 2L / n

Where it shows that frequency depends on speed but wavelength does not.

But can someone provide a conceptual/more_intuitive explanation for this?

Part of my confusion comes from TPR's 2 big rules for waves":

1) When a wave passes into another medium, its speed changes but frequency does not.
2) Speed of wave is determined by TYPE of wave and characteristics of MEDIUM - NOT by the Frequency

which always makes me overly cautious when picking choices in which frequency DOES change.

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[echoyjeff222]

Frequency apparently only changes when you have doppler effect things going on ... any other time, when speed changes, wavelength is the factor that changes. TBR didn't really provide any intuitive explanations, so I sort of memorized that as an empirical fact.

If anyone has a better explanation, I'd like to know as well!

 

[Shirafune]

TBR Physics Book II page 42 # 44
f= nv / 2L and Wavelength = 2L / n

You pretty much summed it up yourself, but maybe this will help.

Frequency usually only depends on the source while the wave speed depends only on the medium. Consequently, wavelength depends on both the source (how fast something generates a wave) and the medium (how fast can the wave travel). It's not exactly the same in this situation. You can think about it this way: frequency is dependent on two things (1) wave speed and (2) length of the pipe. Wavelength is only dependent on the length of the pipe. Increasing temperature increases wave speed because there is a change in medium. Your wave is not traveling from one medium to another medium. You are creating a new wave in a new medium. Given the fact that the length of the pipe doesn't change, wavelength is constant and so an increase in wave speed (v) must lead to an increase in frequency.

As an example in real life, we play woodwind instruments by changing the length of the pipe (either closing or opening up finger holes). Wave speed doesn't change because then the whole system is messed up. For a given length of pipe and a given wavelength, we can get multiple frequencies because our wave speed changes!? That just doesn't make sense. In reality, we change the length of the pipe, which changes frequencies because of a constant wave speed. Temperature is also the reason why players need to tune their instruments differently at different times of the year/at different venues/etc.