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It is a common belief that low frequencies travel longer distances. Indeed, the bass is really what you hear when the neighbor plays his HiFi loud (Woom Woom). Try asking people around, a lot of them believe that low sounds carry longer distances.

But my experience isn't as straightforward. In particular:

  • When I stand near someone who's listening loud music in headphones, it is the high pitched sounds that I hear (tchts tchts), not the bass.
  • When I sit next to an unamplified turntable (the disc is spinning but the volume is turned off), I hear high pitched sounds (tchts tchts), not the bass.

So with very weak sounds, high frequencies seem to travel further?

This makes me think that perhaps low frequencies do not carry longer distances, but the very high amplitude of the bass in my neighbor's speakers compensates for that. Perhaps also the low frequencies resonate with the walls of the building? Probably also the medium the sound travels through makes a difference? Or perhaps high frequencies are reflected more by walls than low frequencies?

I found this rather cute high school experiment online, which seems to conclude that low and high frequencies travel as far, but aren't there laws that physicist wrote centuries ago about this?

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You're confusing multiple things here (may be split the question in 2?). What you hear sitting near the non-amplified turntable is mostly determined by your ear's sensitivity to various frequencies, not some propagation phenomena (check out the diagram: diracdelta.co.uk/science/source/t/h/threshold%20of%20hearing/…). –  oakad Nov 25 '13 at 7:54

5 Answers 5

up vote 16 down vote accepted

Do low frequencies carry farther than high frequencies? Yes. The reason has to do with what's stopping the sound. If it weren't for attenuation (absorption) sound would follow an inverse square law.

Remember, sound is a pressure wave vibration of molecules. Whenever you give molecules a "push" you're going to lose some energy to heat. Because of this, sound is lost to heating of the medium it is propagating through. The attenuation of sound waves is frequency dependent in most materials. See Wikipedia for the technical details and formulas of acoustic attenuation.

Here is a graph of the attenuation of sound at difference frequencies (accounting for atmospheric pressure and humidity):

sound absorption at various frequencies

As you can see, low frequencies are not absorbed as well. This means low frequencies will travel farther. That graph comes from this extremely detailed article on outdoor sound propagation.

Another effect that affects sound propagation, especially through walls, headphones, and other relative hard surfaces is reflection. Reflection is also frequency dependent. High frequencies are better reflected whereas low frequencies are able to pass through the barrier:

sound frequency transmission versus reflection

This is and frequency-based attenuation are why low-frequency sounds are much easier to hear through walls than high frequency ones.


Frequency Loudness in Headphones: The above description apply to sounds that travel either through long distances or are otherwise highly attenuated. Headphones start off at such low intensities already they don't travel long enough distances for attenuation to be a dominate factor. Instead, the frequency response curve of the human ear plays a big role in perceived loudness.

The curves that show human hearing frequency response are called Fletcher–Munson curves:

Fletcher-Munson_curves

The red lines are the modern ISO 226:2003 data. All the sound along a curve is of "equal loudness" but as you can see, low frequencies must be much more intense to sound equally as loud as higher frequency sounds. Even if the low frequencies are reaching your ear, it's harder for you to hear them.

Headphone sound is doubly compounded by the difficulty of making headphones with good low-frequency response. With loudspeakers you can split the job of producing frequencies among a subwoofer, a midrange speaker, and a tweeter. For low frequencies subwoofers are large and have a resonating chamber which simply isn't an option with headphones that must produce a large range of sound frequencies in a small space. Even a good pair of headphones like Sennheiser HD-650 struggle with lower frequencies:

headphones frequency response

So if it sounds like high frequencies travel farther with headphones, it's because headphones are poor at producing low frequencies and your ear is poor at picking them up.

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Constructive comments on a downvote are appreciated. –  Brandon Enright Nov 25 '13 at 7:48
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Could you explain why we usually hear only high-frequency noises from other people's headphones? –  innisfree Nov 25 '13 at 11:36
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Thanks for your very nice answer, @BrandonEnright, but that does not explain why I the headphone sounds are balanced (I mean with the right balance between low and high frequencies) from very near (headphones on) and not at a larger distance. From your first diagram above, we would expect that the higher frequencies should be attenuated more than the low frequencies, so I should hear only low frequencies when the headphones are farther away. shouldn't I? –  Max Nov 25 '13 at 12:20
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@innisfree I added some details about headphones –  Brandon Enright Nov 25 '13 at 18:45
    
Does diffraction not play a role as well? Bass sounds have wavelength about the size of the objects and waveguides in their path, whereas higher sounds are progressively deeper into the ray optics regime. –  Emilio Pisanty Nov 25 '13 at 20:41

In addition the points made in Brandon enright's excellent answer, you need to consider that sound sources aren't really idealised point sources. Depending on the application, you can shape the speaker(s) so you have cylindrical waves, or dipole waves, or sections of a monopole wave ..., or a combination of several patterns.

Normal headphones are basically dipole speakers, and especially for bass frequencies (wavelength much larger than the speakers) this describes their behaviour well. So the amplitide decreases $\propto 1/ r^4$. At higher frequencies, they also have some monopole components which decay more slowly, with the familiar inverse-square. So if you're listening from far away, you'll mostly hear those treble frequencies and little or no bass. OTOH, while wearing the headphones there's little difference since you're in the near field where neither frequency range has decayed substantially at all.

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More detail here could be useful - how big is a typical headphone (or earphone) diaphragm? Can a diaphragm really produce monopole sound? How far does the near field extend? And of course, as mentioned below, in the far field all frequencies obey the inverse square law. –  akrasia Aug 24 at 17:58
    
@akrasia: the near-field includes the eardrums (or at least the ear canal: once you're in a waveguide, all works differently anyway!). That's basically all that's relevant here, and it follows easily from the effective size of the diaphragm: larger than the distance to the ears. Ear-plugs are right in the ear canal themselves, so for those it's obviously true. –  leftaroundabout Aug 24 at 22:30

Another thing that happens that can lead you to think that low frequency sounds attenuate quicker is that if you record yourself one time being close to the microphone and another time being farther away, you'll notice that the farther you are the more the lowest frequencies are picked up. This is due to the proximity effect and not to the low frequency sounds being attenuated.

http://en.wikipedia.org/wiki/Proximity_effect_(audio)

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I think it has nothing to do with the frequency, but usual sounds consist of many fundamental frequencies and their harmonics, and usually you would have sounds built with such a formula like

$$S(t)=\sum_{N=1}^\infty \frac{1}{N}\cos{N\omega t}.$$

So you see, lower frequencies would usually have higher amplitudes, and live longer.

You can prove to yourself that sound signals with such a structure are much more pleasant to listen to than something with equal amplitudes on all frequencies. Check this video, which has a nice way to present the idea of playing sounds using functions with Mathematica.

Hope this helps.

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Sound attenuation is frequency dependent. –  Brandon Enright Nov 25 '13 at 7:50

Wave always carry energy infinite distance. The energy of sound may dissipate along distance by many cause at the same rate in any frequency

Low frequency wave not carry in "longer distance" than high frequency. But it may have less problem in propagate to things. Lower frequency wave tend to pass though bigger object with lesser absorb or reflect. So in this kind of situation, if the environment have many obstruct matter, lower frequency can travel farther than higher frequency

Actually it about wavelength. Both sound and light has the same nature of wavelength propagation. Longer wave tend to pass trough object that has bigger size than length of the wave

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