# Does it take longer for low-frequency sounds to reach a listener?

Assuming a normal earth/air listening environment with a normal speaker and a human listener...

Sound travels in a room when air particle A (near a speaker) collides with air particle B, etc, until air particles near a human's eardrum are collided with to cause the eardrum to vibrate.

A higher frequency tone (1000Hz) would cause particle A to move away from the speaker at a higher velocity than a lower frequency tone (100Hz), which seems to indicate that the 1KHz tone will reach the listener slightly before the 100Hz tone. I'm thinking this because the particles disturbed near the listener will be disturbed sooner by the 1KHz tone. Is this correct, or am I missing something?

• There is a small effect between 10 Hz and 100 Hz, round about 0.1 m/s. Above that, and for the full range of audible-to-humans, the speed of sound is extremely close to constant w.r.t. frequency.
– Dan
Jan 25, 2022 at 3:38

Speed of sound in air is largely independent of frequency (in everyday circumstances, in the hearing range).

To take the reasoning given in the OP: the molecules in the air actually do not propagate very far, but rather collide with other molecules (see, e.g., the discussion in this thread). This is why the sound can be described in hydrodynamic terms, i.e., in terms of quantities average over many millions of molecules, such as the air density and pressure. The speed of sound is then given by $$c=\sqrt{\left(\frac{\partial P}{\partial \rho}\right)_s},$$ i.e., by how fast the pressure responds to the change of density. The difference in the initial velocities of the molecules is thus largely levels out.

I think that you are forgeting that a higher frequency would also make the particles go back faster, with the movement of the speaker's membrane. Sound is a wave, and is the wave propagation velocity the one you are going to measure.

• Are you telling that sound propagation depends on the frequency?
– user130529
Oct 28, 2016 at 20:15
• @claudechuber it depends, indeed, because of the properties of the medium. I'm just proposing a counterexmple to Danaiel Smith's reasoning, to demonstrate that in a first order of aproximation the frequency does not matter, and to explain that he is thinking in sound more like one would think of a particle instead of like a wave. Oct 29, 2016 at 9:53
• In the basic (second order) wave equation, the sound speed does not depend on the frequency, which is the usual way of treating waves propagating in air, and seems to be the assumption made here ("normal earth/air listening environment"). Though I agree that this is only an approximation, and introducing higher order terms can bring dispersion.
– user130529
Oct 29, 2016 at 12:45

The speed of both frequency sounds once they leave the source is same.

But going into too much details - Think about a single pulse of two frequencies. It takes longer to generate the lower frequency pulse as compared to higher frequency pulse. So, the lower frequency pulse last that much longer at the destination. Not because it was moving slower through air, but because it was being generated slower. The longer lasting pulse can give impression of a slower moving pulse.

I have no answer but propose a simple and easy-to-execute experiment to find the answer, since answers given are slightly contradictory or unsure of themselves.

Take a sound generator (such as a boombox or a simple bicycle bell and bicycle horn even) to a place where there is clear reach to a distant wall, at least 2-300 metres away. Sound both at the same time and listen to the echoes coming back. If there is a material difference between speed of propagation between high- and low-frequence sounds, the "faster" sound you should hear slightly before the "slower" sound.

By the way, I don't buy the "longer to generate" theory, typically applied to thunder and how it sounds to the human some distance away. If you are NEAR a lighting striking, you will NOT hear a high frequency first, and then a few seconds later a low frequency sound. They don't get generated later. They both get generated instantaneously. I mean, why would they get different generation time? The lightning does not last seconds, whereas the deep sounds last up to ten seconds some distance away from the lightning to the human ear.

What I think happens is that the deep sounds have a larger propensity to be echoed by the medium itself that carries it. Much like a Pringer-Hoffsteiner effect, the wave itself creates and behaves in an elastic manner, and it does not behave only in a straight-line propagation manner. It pushes the air forward, which will repush some of the sound backward, and which gets pushed forward again. Hence the effect of a longer, much longer rumble of thunder by a lightning, while the high frequency sounds do not have much energy, therefore they have a negligible Pringer-Hoffsteiner effect.

This explanation of lightning does not explain which travels faster, the lower or the higher frequency sound. They may travel at the same speed, but as the deep sounds are elongated, their intensity may be spread, and it may reach the listener at the same time as the high-pitched sound, the high-pitched comes loud as it hasn't lost amplitude due to dampening; and the low-frequency may initially arrive at the same time as the high, but due to dampening and its energy dispersed into a longer time interval, it may be muffled or just not attended to by the human ear.