# Wavelengths at a distance

## Homework Statement

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If you hear music in the distance, would you be more likely to hear the treble or the bass notes of the music? Using your knowledge of diffraction, explain your answer.

## The Attempt at a Solution

It would be more likely to hear the bass notes for a number of reasons. Bass notes have a lower frequency than treble notes, and since wavelength is inversely proportional to frequency, a lower frequency would have a higher wavelength. Since diffraction increases with a larger wavelength, a wave with a greater wavelength would diffract more, thus the bass notes would spread out more, than the treble notes, making it more likely for one to hear a bass note from a distance than a treble note.

I believe all of this is correct, I'm just not sure if I'm presenting it in the correct way. Any feedback is appreciated.

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I think this is incorrect. (I could be wrong). Yes, you will hear the bass notes better, but not for the reason you gave. ## \\ ## One suggestion is to read about Rayleigh scattering, which occurs with light from inhomogenities in the atmosphere, and the scattering is inversely proportional to the 4th power of the wavelength. See https://en.wikipedia.org/wiki/Rayleigh_scattering The Rayleigh scattering explains why the daytime sky appears blue. To explain the blue sky, red light (which has a wavelength almost twice that of the blue), travels basically in straight lines and doesn't get scattered appreciably, while the blue light gets scattered a very significant amount. ## \\ ## Rayleigh scattering also explains why the sun, when viewed on the horizon , (where the light from it need to travel through about 100 or more miles of atmosphere to reach us, instead of the ten miles or thereabouts of atmosphere when it is overhead), appears red during a sunrise or sunset. (Most of the blue light gets Rayleigh scattered out over a 100 mile atmospheric path and doesn't reach us directly). ## \\ ## I think a similar type of result is likely to be found when sound travels through the atmosphere. (They may call it "diffraction", but a better name for it is "scattering").

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I think this is incorrect. (I could be wrong). Yes, you will hear the bass notes better, but not for the reason you gave. ## \\ ## One suggestion is to read about Rayleigh scattering, which occurs with light from inhomogenities in the atmosphere, and the scattering is inversely proportional to the 4th power of the wavelength. See https://en.wikipedia.org/wiki/Rayleigh_scattering The Rayleigh scattering explains why the daytime sky appears blue. To explain the blue sky, red light (which has a wavelength almost twice that of the blue), travels basically in straight lines and doesn't get scattered appreciably, while the blue light gets scattered a very significant amount. ## \\ ## Rayleigh scattering also explains why the sun, when viewed on the horizon , (where the light from it need to travel through about 100 or more miles of atmosphere to reach us, instead of the ten miles or thereabouts of atmosphere when it is overhead), appears red during a sunrise or sunset. (Most of the blue light gets Rayleigh scattered out over a 100 mile atmospheric path and doesn't reach us directly). ## \\ ## I think a similar type of result is likely to be found when sound travels through the atmosphere. (They may call it "diffraction", but a better name for it is "scattering").

Hi Charles,

Thanks for the great link. So you think it has more to do with "scattering" than "diffraction"? The reason I used diffraction is because that is the terminology used mostly in my textbook.

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Hi Charles,

Thanks for the great link. So you think it has more to do with "scattering" than "diffraction"? The reason I used diffraction is because that is the terminology used mostly in my textbook.
That is what I would have to believe. I have very limited experience with acoustics, but I believe these two cases (light waves and sound waves) are similar. Meanwhile, diffraction and scattering are closely related. In acoustics, they very well might refer to it as diffraction effects that are occurring when the sound is propagating through the air. ## \\ ## Editing: Attenuation (loss of energy) that occurs is usually due to a combination of absorption and scattering. In addition, as the sound propagates, the wave front normally expands as it travels, resulting in lower energy at the receiver as the receiver is moved farther away from the source. The attenuation is normally considerably more for the shorter wavelengths, while this second feature that results in reduced volume, (the expanding wave front), is normally similar for most wavelengths.

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That's quite interesting. I didn't think to account for the loss of energy, but that completely makes sense. Thank you for all of your help in improving my answer.

That's quite interesting. I didn't think to account for the loss of energy, but that completely makes sense. Thank you for all of your help in improving my answer.
I did some research on diffraction and scattering, and believe this explains the differences well.

"Diffraction is a coherent process and scattering is an incoherent process. Diffraction requires that the surface/medium is regular on distances comparable to the wavelength of the light being diffracted. In comparison, when an interface/surface is rough on length scales comparable to the wavelength of the light, the light will scatter."

PS: Physicists often use the term scattering for coherent processes too.

Source: https://www.quora.com/What-is-the-difference-between-scattering-and-diffraction

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