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

• jwkhjang
In summary, temperature change affects the speed of sound, which in turn affects the frequency and wavelength of sound waves. However, in the case of sound traveling through a tube, the resonance wavelengths remain the same but the frequency changes due to the change in speed of sound. In general, the dominant effect of temperature change on sound is the change in speed of sound.
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?

jwkhjang said:
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?
Yes.

jwkhjang said:
I was curious because if temp. increases, the frequency increases
Why would the frequency change with temperature? I assume that you are talking about sound waves traveling through some medium.

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

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?

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.

DrClaude
The intensity of wavelength increases with increase in temp and the wavelength itself decreases so the wavelength is inversely proportional to temp and the frequency is directly proportional to temp, but in case of sound waves frequency is not effected the change in speed is due to the fact that the average kinetic energy of the molecules of the medium is directly proportional to temp.

## What is the relationship between frequency, wavelength, and temperature?

The relationship between frequency, wavelength, and temperature can be described by the formula c = λv, where c is the speed of light, λ is the wavelength, and v is the frequency. This formula indicates that as the frequency of a wave increases, its wavelength decreases. Additionally, as the temperature increases, the speed of light also increases, which can affect the wavelength and frequency of a wave.

## How does temperature affect the speed of light?

According to the formula c = λv, an increase in temperature results in an increase in the speed of light. This is because temperature affects the density and refractive index of the medium through which light travels. As the temperature increases, the molecules in the medium move faster, causing them to scatter and absorb light more, resulting in a slower speed of light. Similarly, lowering the temperature can result in a decrease in the speed of light.

## What is the relationship between temperature and the wavelength of a wave?

Temperature can indirectly affect the wavelength of a wave through its influence on the speed of light. As mentioned before, an increase in temperature can result in an increase in the speed of light, which in turn can affect the wavelength of a wave. As the speed of light increases, the wavelength decreases, and vice versa.

## How does temperature affect the frequency of a wave?

Similar to its effect on wavelength, temperature can indirectly impact the frequency of a wave through its influence on the speed of light. As the temperature increases, the speed of light increases, causing the frequency of the wave to also increase. This is because the speed of light and frequency have an inverse relationship, meaning that as one increases, the other decreases. Therefore, an increase in temperature can result in a higher frequency of a wave.

## Can temperature affect the behavior of electromagnetic waves?

Yes, temperature can affect the behavior of electromagnetic waves. As mentioned before, temperature can impact the speed of light, which in turn can affect the wavelength and frequency of a wave. Additionally, temperature can also affect the absorption and scattering of electromagnetic waves, which can alter their behavior. This is why studying the effects of temperature on electromagnetic waves is important in various fields such as astronomy and meteorology.

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