# Can sound fall?

1. May 25, 2012

### jetwaterluffy

I know that light can, because otherwise black holes wouldn't exist. But can sound fall? And are there any effects caused by this. By doing a rough calculation, if sound could fall, sound would have a maximum vertical range of about 5km. Do we see this in real life?

2. May 25, 2012

### Staff: Mentor

Yes, sound is just a vibration in some material. If I pluck a guitar string and drop it the sound is falling. People think of this more in the context of sound being bent. As an example, historians have said that some battles were lost due to sound refraction around or over some place and the general didn't hear the start of the battle and didn't do his part.

http://www.acoustics.org/press/136th/ross.htm [Broken]

Last edited by a moderator: May 6, 2017
3. May 25, 2012

### A.T.

The pressure gradient can cause bending/refraction. So there is an indirect effect of gravity on sound, but it is not an acceleration at g like for massive objects and light.

I doubt it, you cannot assume g acceleration. Any balloonist here?

4. May 25, 2012

### jetwaterluffy

Yeah, but light is just an oscillation in an electromagnetic feild.

5. May 25, 2012

### D H

Staff Emeritus
That is a very Newtonian way of looking at black holes. You cannot apply Newtonian mechanics in this domain. Newtonian mechanics is only valid in domains of smallish velocities, smallish masses. Black holes are far removed from the domain where Newtonian mechanics is valid. Black holes and Newtonian gravity just don't mix.

A better way of looking at black holes is that the extreme mass curves spacetime to such an that every direction is down (toward the center) inside the event horizon. Our puny Earth curves spacetime to a much lesser extent.

No.

No.

Were your thesis correct, the speed of sound at some altitude would depend on the altitude of the emitter. It doesn't. The speed of sound depends solely on local conditions. Suppose you are the top of the Tokyo Sky Tree and you hear some sound. That sound wave is moving at the local speed of sound. It doesn't matter if the source was a jet passing a kilometer overhead or something making a very large noise 634 meters below.

Acoustic shadows have nothing to do with sound falling.

Last edited by a moderator: May 6, 2017
6. May 25, 2012

### Staff: Mentor

DH I would disagree with your comment about acoustic shadows. Sound can rise and fall based on air column movement. On really hot days, you might not be able to hear traffic on a nearby road because the sound is refracted upward.

Similarly, with a falling column of air sound would fall with it that is why I cited the Civil War article. Sound speed is affected by the medium, the temperature, the pressure and a number of other more arcane factors.

7. May 25, 2012

### D H

Staff Emeritus
The speed of sound is mostly dependent on temperature, somewhat dependent on the medium (packets of air with different makeup will have different gammas, different molar masses), plus some other arcane factors due to air not being an ideal gas. Plus of course wind velocity. The speed of sound is of measured with respect to the (potentially moving) air mass.

That's a bit irrelevant to the topic at hand, though, as are your acoustic shadows. What is relevant is that there is only one speed at which a sound wave of a given frequency will travel traveling through a given packet of air. There is no such thing as "tired sound", sound that is moving slower because it has gained altitude. This "tired sound" (sound waves slowing down with gain in altitude) is what is needed to get that "maximum vertical range of about 5km" referenced in the original post.

8. May 25, 2012

### Ken G

Yes, I think the question is about sound falling in air, not sound falling with air, or due to refraction by differences in air density. To lowest order, sound moves in the frame of the air, so does not fall at "g" if the air is stationary. Of course if you drop an enclosed box of air, any sound within that box will fall with the box, and of course sound will refract if it encounters density differences, but whether those differences are due to gravity or something else it won't care.

However, there must be higher-order effects of gravity on sound. For example, it must be true that the frequency of sound does "tire" if the sound propagates upward (but not to the extent in the OP-- the sound speed does not decelerate like g, it's a higher order effect than that). Imagine a tuning fork and a light clock at some point deeper in a gravity well than the point from which their action is being regarded. Certainly the ratio of the ticking up the light clock and the oscillating of the tuning fork is an invariant ratio. So if the light clock is regarded as ticking slow, then the tuning fork must also be regarded as sending out a lower frequency sound signal than how it is regarded at its source. Hence, the sound must be perceived as shifting to lower frequency as it is observed by higher and higher observers, maintaining the same frequency ratio with a beam of light doing the same thing.

Last edited: May 25, 2012
9. May 25, 2012

### Staff: Mentor

It would be interesting to do an experiment measuring a sound source from above and below to see if a Doppler effect could be detected that is not due to air density.

10. May 25, 2012

### Ken G

Air density affects direction and amplitude, but not frequency. But I doubt the effect I described would ever be measurable, because there is probably not the necessary precision in the creation and measurement of sound frequency.

11. May 25, 2012

### K^2

Wave propagation 101. As the energy of the signal changes, it's the wavelength that becomes different. And yes, the wavelength will change as sound travels vertically. Most of it is due to pressure/temperature changes, which are also due to gravity. But energy of the sound wave will also change.

It's only the frequency that has to stay the same, to within gravitational red-shift.

Moving any form of energy against gravitational potential requires work. Sound does carry energy. Sound going up against gravitational potential will, therefore, lose energy. Sound traveling in parallel to the ground will be attracted towards the ground and "fall".

12. May 26, 2012

### mrspeedybob

The frequency will be higher below the source and lower above the source due to time dilation. Less time passes deeper in the gravity well, but the same number of vibrations occur, so the frequency is higher. Higher frequency means higher energy so sound will gain energy as it moves down and lose energy as it goes up. This is exactly the same reason that light "falls".

13. May 26, 2012

### D H

Staff Emeritus
Find one book, one journal article that discusses your concepts.

The speed of sound in the Earth's atmosphere is many orders of magnitude smaller than the speed of light, and the Earth's radius is many orders of magnitude larger than the Earth's Schwarzschild radius. Sound propagation in the Earth's atmosphere is safely in the Newtonian limit. Certainly the relativistic effects described by Ken G must exist, but they are immeasurably small.

In the Newtonian limit, gravitation is a conservative force. In an ideal gas, sound is massless and is non-dissipative. Put these together and there is no energy loss as sound propagates upward. At least not in an isothermal, uniformly mixed ideal gas.

Our atmosphere is not isothermal, and is not uniformly mixed (H20 is the primary culprit), and is not ideal. The non-isothermal nature means that the speed of sound varies with altitude. For the most part, it decreases with increasing altitude because the environmental lapse rate is generally positive (temperature decreases with altitude). Sound refracts in the direction of decreasing speed of sound. For the most part, sound "falls" up, not down.

Our atmosphere is not ideal. Sound dissipates and loses energy due to this non-ideal behavior. Example: Thunder from far away sounds different than thunder from a nearby storm. These non-ideal effects will mask any relativistic effects. While those relativistic effects most certainly must exist, they are so small and so completely masked by other effects as to be unobservable.

One last point regarding the maximum vertical range of about 5km alluded to in the original post. Sound refracts downward off of temperature inversions. The stratosphere is warmer than the upper troposphere. The tropopause is a permanent temperature inversion. This can act to form the equivalent of a waveguide for loud, low frequency sounds. People in England occasionally heard the fighting on the continent during World War II because the sounds from that fighting reflected off the stratosphere 50 km or so high. Another example of the same phenomenon is reported here: http://www.agu.org/pubs/crossref/1965/JZ070i022p05499.shtml.

14. May 26, 2012

### K^2

In Newtonian limit, the only effect is on medium. But the primary reason atmosphere is not isothermal or isobaric is still gravity. You cannot have sound propagation without lensing if there is a gravitational field involved. Assumption of uniform atmosphere is inherently flawed if work has to be done to raise or lower a volume element. If you are talking about effects of gravitational field on sound propagation, you have to take into consideration the fact that speed of sound varies with altitude primarily due to gravity. (Yes, up until you get into troposphere where new phenomena take place.)

15. May 27, 2012

### Ken G

I'm with D H. I don't think it's true that the speed of sound varies in some direct or inescapable way due to gravity, it primarily varies due to temperature and mean molecular weight differences. Yes, the atmosphere is a complex system, acted on by gravity, and involves many factors that produce differences in sound speed. But there's nothing fundamental about gravity that must produce sound speed differences-- one can imagine, in principle, an isothermal and homogeneous gas that has a pressure and density gradient due to gravity, but no significant variation at all in the sound speed. Mostly what changes in response to density variations is the amplitude of the wave, but if it stays in the linear regime (small amplitude), then it's still going to propagate at the same speed if T is the same and the gas is homogeneous.

16. May 27, 2012

### D H

Staff Emeritus
Gravity is not the primary reason the atmosphere is not isothermal. Take away the fact the the atmosphere is heated from below, cooled from above, or take away the greenhouse gases and you get an isothermal atmosphere.

However, the primary reason the atmosphere exists at all is gravity. So in that sense, of course gravity plays a role in sound propagation. Beyond that, gravitation does not play a role (other than immeasurable relativistic effects) in the propagation of sound. Find one reference that says it does.

17. May 28, 2012

### K^2

Not even close. Air cools as it expands. A convection current going up, cools. Convection current going down, heats up. The energy for this comes from work by/against gravity. You can ignore both the effects you describe, only use adiabatic expansion, and still get a very good estimate for temperature variation with altitude for the first few km. (Would you like some plots?) In upper atmosphere, like I said, more interesting things happen. The inversion in troposphere, by the way, is a pretty good indication that atmosphere isn't just being heated from bellow.

18. May 28, 2012

### D H

Staff Emeritus
Wrong. Take away the heating from below and cooling from above and you get an isothermal atmosphere. Imagine a tall, thermally isolated, gas-filled cylinder that is oriented vertically in a gravity field. The condition that maximizes entropy is isothermal conditions, even with that gravity field. An atmosphere with a non-zero lapse rate would allow violations the second law of thermodynamics. The reason we get a lapse rate in our real atmosphere is that it isn't an isolated system (it is heated from below, cooled from above) and because it is far from the equilibrium state. It doesn't have a chance to reach that equilibrium state.

19. May 28, 2012

### K^2

You don't need heating from bellow cooling from above, still. Yes, you need mixing. But uneven surface heating is sufficient. In fact, day/night cycle is sufficient, because that already produces convective currents. Heating AND cooling can both take place at the surface.

Like I said, adiabatic model matches the actual atmospheric temperature. You don't need any net heat flow through atmosphere, which is, in fact, very minor compared to heat exchange at the surface.

And yes, this would be a violation of thermodynamic laws if there was no energy input. But there is. You have the Sun driving the convection currents, which basically means you have an AC cycle in atmosphere. Power for it comes from Sun, but the PV changes come from gravitational potential. You can't have an atmosphere with this temperature profile without gravitational potential.

20. May 28, 2012

### Ken G

The reason the atmospheric temperature gradient equals the adiabatic lapse rate is not because of gravity, it is because of the greenhouse effect. The greenhouse effect attempts to produce a temperature gradient that exceeds what is convectively stable, so convection appears. The convection involves buoyancy, so gravity, but it is not there inescapably because of gravity-- as D H said, it is easy to imagine a situation where you have gravity but no convection. Just take away the greenhouse gases! It is as we have been saying-- there is just no direct or inescapable connection between the presence of strong gravity and the presence of a changing sound speed, nor is there a requirement that temperature must fall as you go up (it doesn't in some layers of the atmosphere, in fact), nor is there a requirement that the sound speed must fall as you go up against gravity. Our own atmosphere proves all these points.