# B What's the relationship btw frequency, wavelength, and temp?

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1. Feb 1, 2017

### jwkhjang

I'm currently studying wavelength and frequency and I've learned about the equation v= f*Lambda. What will happen if temperature is changed? I know that speed of the sound will increase. Does it mean that wavelength will also increase? I was curious because if temp. increases, the frequency increases which mean is that both speed of the sound and the temp will increase. So will the wavelength stay the same?

2. Feb 1, 2017

### Staff: Mentor

Yes.

Why would the frequency change with temperature? I assume that you are talking about sound waves traveling through some medium.

3. Feb 1, 2017

### jwkhjang

Thanks for answering! Oh I'm investigating the effect of temperature change on the tune (frequency) of a brass instrument (only for vibrating air columns). I've learned that the tune of a pitch changes slightly due to the change in temp. Then will the wavelength stay the same?

4. Feb 1, 2017

### nasu

In this case the pitch depends on the "matching" between the size of the tube and some fraction of the wavelength of the standing waves established in the tube.
If the change in the dimensions of the tube with temperature is negligible, the resonance wavelengths remain the same but as the speed of sound changes the frequency changes as well.

A more drastic effect you achieve by replacing air with a different gas, with different speed of sound. Like when you inhale helium. Your resonant cavities remain the same so the same wavelengths will resonate but the pitch of your voice increases.

In the case of temperature increase the tube itself expands a little but possibly the effect of increased speed is larger. You can do some estimates.
The increase in speed of sound in air is about 0.6 m/s for 1 degree Celsius. This is of the order of 0.1%.
The expansion of metals is of the order of 10-5 per degree or 0.001 % . So the effect of speed of sound is the dominant effect.

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