# Force of a sound wave

GBA13
TL;DR Summary
Can a sound wave be approximated as a force? If so, how?
Hello,

I am going to be doing a project in which I'll be looking at how sound waves change the shape of an object. Specifically how sound waves can compress something. My question is, can I approximate a sound wave as a force in this case? I know a sound wave is much more complicated than a force but if I know the dB and frequency of a sound, and the area of the surface the sound is hitting, can I calculate the force acting on the surface due to the sound wave?

EDIT: I will likely be looking at something akin to a gun shot, so an impluse, if that makes any difference.

Thank you!

Mentor
There's a difference between sound waves and a compressed air pulse. Even a pulse of sound will be a longitudinal pressure oscillation, so it will cause vibrations in the target, not just a compression.

You could use an air blaster like one of these, assuming you can still find them...

https://www.hakes.com/Image/MediumRes/73189/2/image.jpg

anorlunda
GBA13
There's a difference between sound waves and a compressed air pulse. Even a pulse of sound will be a longitudinal pressure oscillation, so it will cause vibrations in the target, not just a compression.

You could use an air blaster like one of these, assuming you can still find them...

https://www.hakes.com/Image/MediumRes/73189/2/image.jpg
View attachment 243179

Thank you for your response, berkeman. I see what you're saying. Is it not at all appropriate to consider a sound wave to act on a object like a compressed air pulse would? I was hoping to be able to simulate the effect of a gunshot-type noise by exerting a force to the object but does that just not make sense, physically?

Mentor
GBA13
It is an oscillating longitudinal wave. A single gunshot would look something like this (you can see the decaying oscillations):

http://www.flashkit.com/imagesvr_ce...shot-Farbod_A-8301/gun_shot-Farbod_A-8301.png
View attachment 243180

To get more of a pulse, you should look into the subject of Blast Waves. @Dr. Courtney is our local expert on blast waves.

Okay thank you, I understand what you're saying. It seems like my hope to be able to simply apply a force seems like a no go (it came out of the idea that sound can be measured in Pa or N/m2, so a force could be extracted). Moving away from physical simulations, are there any computer simulation packages that can model how a longitudinal wave interacts with objects/surfaces etc.?

Gold Member
The tricky part is distinguishing between instantaneous forces and net momentum transfer. Lots of sounds have time average forces very close to zero, because the pressure is negative over time as much as it is positive. At longer distances from the source, this is true of gun shot reports and blast waves also.

But the closer one gets to the source, the more the time varying pressure of a gun shot or a blast wave can and will have a net positive momentum transfer.

Have a look at this paper where we used a simple pump air pistol (without projectiles) and a short piece of pipe to simulate laboratory blast waves. I assure you, there will be a momentum transfer to something like a ping pong ball placed at the far end of the pipe. If you look at the pressure vs. time curves in Figure 2, you can see that the pressure is mostly positive. The force on the ball would be the pressure times the cross sectional area of the pipe. Integrating the resulting force over time would give you the impulse - which is the same as the momentum transfer.

https://arxiv.org/ftp/arxiv/papers/1502/1502.06112.pdf

Asymptotic and berkeman
GBA13
The tricky part is distinguishing between instantaneous forces and net momentum transfer. Lots of sounds have time average forces very close to zero, because the pressure is negative over time as much as it is positive. At longer distances from the source, this is true of gun shot reports and blast waves also.

But the closer one gets to the source, the more the time varying pressure of a gun shot or a blast wave can and will have a net positive momentum transfer.

Have a look at this paper where we used a simple pump air pistol (without projectiles) and a short piece of pipe to simulate laboratory blast waves. I assure you, there will be a momentum transfer to something like a ping pong ball placed at the far end of the pipe. If you look at the pressure vs. time curves in Figure 2, you can see that the pressure is mostly positive. The force on the ball would be the pressure times the cross sectional area of the pipe. Integrating the resulting force over time would give you the impulse - which is the same as the momentum transfer.

https://arxiv.org/ftp/arxiv/papers/1502/1502.06112.pdf

Hi @Dr. Courtney,
Thank you for that insight, that's really interesting. Do you know of somewhere more I could read more about the net momentum transfer in gun shots?
Also, you mention the distance from the source as being clearly important. For typical gun shot would you be able to give a guess as the distance that there would still be a significant net positive transfer? I'm wondering if I looked at the blast wave from the muzzle of a rifle if there would be a net positive transfer at the user's ear, for example. My second thought it whether the open air would be a big difference compared to the tube you used for you work in the paper that you kindly provided. Any insights you could offer would be very helpful!
Thank you very much!

Gold Member
Hi @Dr. Courtney,
Thank you for that insight, that's really interesting. Do you know of somewhere more I could read more about the net momentum transfer in gun shots?
Also, you mention the distance from the source as being clearly important. For typical gun shot would you be able to give a guess as the distance that there would still be a significant net positive transfer? I'm wondering if I looked at the blast wave from the muzzle of a rifle if there would be a net positive transfer at the user's ear, for example. My second thought it whether the open air would be a big difference compared to the tube you used for you work in the paper that you kindly provided. Any insights you could offer would be very helpful!
Thank you very much!

A Google Scholar search for muzzle blast will bring up a number of interesting and relevant papers. Here's one:

https://apps.dtic.mil/dtic/tr/fulltext/u2/688789.pdf#page=145
My expert guesstimate is that most small arms will produce a net positive momentum transfer for a peak distance from 1 to 10 feet. Stuff like a 22 LR will have a shorter range, stuff like a 300 Win Mag will be a longer range. But the blast field is not the same in every direction and tends to be smaller behind the gun than in front. Devices called muzzle brakes increase the blast to the sides.

In our experiment with the air pistol and the pipe, the pipe keeps the blast wave from spreading out over a much larger area and decreasing quickly with distance. It also reduces the forward flow of the compressed air so that there is less blast wind relative to the blast wave.

Measuring how blast waves compress something is a tricky business and hard to measure with easily available equipment for an amateur enthusiast. However, momentum transfer is easy to measure with a pendulum. I'd suspend a test sphere on a string and use a video camera to record the sphere's motion after the momentum transfer event. Simple physics formulas will relate the peak height the pendulum reaches to the momentum transfer it received in the event.

GBA13
Thanks once again, @Dr. Courtney, this has been really useful.

One final thing I am just wondering about: when someone is deafened by a gun shot or explosion, is it the sound wave or the explosive blast wave that actually damages the ear? As someone can loose hearing from long term exposure it's clear that sound waves at dangerous levels can damage the ear drum but if, for example, a solider is standing too close to a howitzer without hear protection what is it that will actually cause hearing damage?

Gold Member
Thanks once again, @Dr. Courtney, this has been really useful.

One final thing I am just wondering about: when someone is deafened by a gun shot or explosion, is it the sound wave or the explosive blast wave that actually damages the ear? As someone can loose hearing from long term exposure it's clear that sound waves at dangerous levels can damage the ear drum but if, for example, a solider is standing too close to a howitzer without hear protection what is it that will actually cause hearing damage?

Either can be damaging, and most of the available data is in the frequency domain. See:
https://apps.dtic.mil/dtic/tr/fulltext/u2/a162526.pdf
The thresholds for a given level of damage or impairment tend to be lower at lower frequencies (< 1000 Hz) than they are for higher frequencies. This indicates that if the peak pressure stays high for more than a millisecond before it drops, then the peak pressure needed to damage hearing is lower. The blast portion of a Howitzer will last longer than 1 ms at closer distances to the thing.

Gold Member
From a classical perspective sound is measured in Intensity (I) which is Power/Area. Sound pressure level is measured in decibels (##\log_{10} \frac I I_o##)