Forums

Sound Intensity

Started by HardySpicer August 21, 2007
We are often told that sound intensity (I assume Power) goes down as
the inverse square of distance. However, I believe this is also
frequency dependent (as with e/m waves). What is the equation for a
sound source received at a distance d with frequency f say? I read
somewhere that low frequency sound (say 50 Hz or so) will travel vast
distances and is also humidity and temperature dependent. It mus be
something like

I=I0.exp(-alpha.d)

where I0 and I are the initial and final intensities, d is distance
and alpha is freq dependent. How is alpha found?

Thanks

Hardy

HardySpicer wrote:
> We are often told that sound intensity (I assume Power) goes down as > the inverse square of distance. However, I believe this is also > frequency dependent (as with e/m waves). What is the equation for a > sound source received at a distance d with frequency f say? I read > somewhere that low frequency sound (say 50 Hz or so) will travel vast > distances and is also humidity and temperature dependent. It mus be > something like > > I=I0.exp(-alpha.d) > > where I0 and I are the initial and final intensities, d is distance > and alpha is freq dependent. How is alpha found?
The attenuation of sound with distance *in the earth's atmosphere* depends on more than the free-space propagation. Refraction and diffraction play a large part. Low frequencies that originate at the surface tend to hug the surface. Their long wavelength make the terrain acoustically smooth, while at higher frequencies, surface irregularities scatter more effectively. Refraction is also important. One can often see lightning over a flat surface like a large lake or extended grassland, yet hear no thunder. The thunder is there, but refraction due to different air density as a function of height bends the sound so that it passes overhead. An observer on a tower or rooftop can hear thunder from much further away. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
HardySpicer wrote:
> We are often told that sound intensity (I assume Power) goes down as > the inverse square of distance. However, I believe this is also > frequency dependent (as with e/m waves). What is the equation for a > sound source received at a distance d with frequency f say? I read > somewhere that low frequency sound (say 50 Hz or so) will travel vast > distances and is also humidity and temperature dependent. It mus be > something like > > I=I0.exp(-alpha.d) > > where I0 and I are the initial and final intensities, d is distance > and alpha is freq dependent. How is alpha found? > > Thanks > > Hardy >
Inverse Square Law, General http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html "Being strictly geometric in its origin, the inverse square law applies to diverse phenomena. Point sources of gravitational force, electric field, light, sound or radiation obey the inverse square law. Attenuation (scattering and absorption) may be factors in light, sound or radiation. http://en.wikipedia.org/wiki/Attenuation
On Aug 22, 11:51 am, Sam Wormley <sworml...@mchsi.com> wrote:
> HardySpicer wrote: > > We are often told that sound intensity (I assume Power) goes down as > > the inverse square of distance. However, I believe this is also > > frequency dependent (as with e/m waves). What is the equation for a > > sound source received at a distance d with frequency f say? I read > > somewhere that low frequency sound (say 50 Hz or so) will travel vast > > distances and is also humidity and temperature dependent. It mus be > > something like > > > I=I0.exp(-alpha.d) > > > where I0 and I are the initial and final intensities, d is distance > > and alpha is freq dependent. How is alpha found? > > > Thanks > > > Hardy > > Inverse Square Law, General > http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html > > "Being strictly geometric in its origin, the inverse square law > applies to diverse phenomena. Point sources of gravitational force, > electric field, light, sound or radiation obey the inverse square > law. > > Attenuation (scattering and absorption) may be factors in light, > sound or radiation. > http://en.wikipedia.org/wiki/Attenuation
Yes thanks, I saw that web page when I searched but it looked like a basic Physics page - it had no info on frequency. If you look at it it appears as if low and high frequencies behave the same - they don't. eg microwaves may well follow an inverse square law but they won't travel as far as an 100MHz signal.
On Aug 22, 11:30 am, Jerry Avins <j...@ieee.org> wrote:
> HardySpicer wrote: > > We are often told that sound intensity (I assume Power) goes down as > > the inverse square of distance. However, I believe this is also > > frequency dependent (as with e/m waves). What is the equation for a > > sound source received at a distance d with frequency f say? I read > > somewhere that low frequency sound (say 50 Hz or so) will travel vast > > distances and is also humidity and temperature dependent. It mus be > > something like > > > I=3DI0.exp(-alpha.d) > > > where I0 and I are the initial and final intensities, d is distance > > and alpha is freq dependent. How is alpha found? > > The attenuation of sound with distance *in the earth's atmosphere* > depends on more than the free-space propagation. Refraction and > diffraction play a large part. Low frequencies that originate at the > surface tend to hug the surface. Their long wavelength make the terrain > acoustically smooth, while at higher frequencies, surface irregularities > scatter more effectively. > > Refraction is also important. One can often see lightning over a flat > surface like a large lake or extended grassland, yet hear no thunder. > The thunder is there, but refraction due to different air density as a > function of height bends the sound so that it passes overhead. An > observer on a tower or rooftop can hear thunder from much further away. > > Jerry > -- > Engineering is the art of making what you want from things you can get. > =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF This is the paper I read the info from - the non-labeled equation after equation 1 (not eq 2!) http://www.sandv.com/downloads/0410vino.pdf
HardySpicer wrote:
> On Aug 22, 11:51 am, Sam Wormley <sworml...@mchsi.com> wrote: >> HardySpicer wrote: >>> We are often told that sound intensity (I assume Power) goes down as >>> the inverse square of distance. However, I believe this is also >>> frequency dependent (as with e/m waves). What is the equation for a >>> sound source received at a distance d with frequency f say? I read >>> somewhere that low frequency sound (say 50 Hz or so) will travel vast >>> distances and is also humidity and temperature dependent. It mus be >>> something like >>> I=I0.exp(-alpha.d) >>> where I0 and I are the initial and final intensities, d is distance >>> and alpha is freq dependent. How is alpha found? >>> Thanks >>> Hardy >> Inverse Square Law, General >> http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html >> >> "Being strictly geometric in its origin, the inverse square law >> applies to diverse phenomena. Point sources of gravitational force, >> electric field, light, sound or radiation obey the inverse square >> law. >> >> Attenuation (scattering and absorption) may be factors in light, >> sound or radiation. >> http://en.wikipedia.org/wiki/Attenuation > > Yes thanks, I saw that web page when I searched but it looked like a > basic Physics page - it had no info on frequency. If you look at it it > appears as if low and high frequencies behave the same - they don't. > eg microwaves may well follow an inverse square law but they won't > travel as far as an 100MHz signal. >
In space there is no frequency dependence. The pattern of radiations is the same until you start to take into consideration such things as absorption, scattering, refraction, reflection and wave-guide effects. Look what astronomers have to deal with for various frequencies (wavelengths) of electromagnetic radiation. http://www.mhhe.com/physsci/astronomy/fix/student/chapter6/06f28.html
"HardySpicer" <gyansorova@gmail.com> wrote in message
news:1187733452.719370.65750@l22g2000prc.googlegroups.com...
> We are often told that sound intensity (I assume Power) goes down as > the inverse square of distance. However, I believe this is also > frequency dependent (as with e/m waves). What is the equation for a > sound source received at a distance d with frequency f say? I read > somewhere that low frequency sound (say 50 Hz or so) will travel vast > distances and is also humidity and temperature dependent. It mus be > something like > > I=I0.exp(-alpha.d) > > where I0 and I are the initial and final intensities, d is distance > and alpha is freq dependent. How is alpha found?
For the small intensities, the propagation can be approximated as the inverse square law times exp(-distance/decay_const). The decay_const can be found from the thermodynamic considerations; it is at the order of 10m at 1kHz in the dry air at normal conditions. The decay_const is inverse proportional to the square root of the frequency. It is a lot more complicated for the high intensities when there is a noticeable macroscopic movement of the air. The nonlinear effects come into play. Vladimir Vassilevsky DSP and Mixed Signal Consultant www.abvolt.com
HardySpicer wrote:
> On Aug 22, 11:51 am, Sam Wormley <sworml...@mchsi.com> wrote: >> HardySpicer wrote: >>> We are often told that sound intensity (I assume Power) goes down as >>> the inverse square of distance. However, I believe this is also >>> frequency dependent (as with e/m waves). What is the equation for a >>> sound source received at a distance d with frequency f say? I read >>> somewhere that low frequency sound (say 50 Hz or so) will travel vast >>> distances and is also humidity and temperature dependent. It mus be >>> something like >>> I=I0.exp(-alpha.d) >>> where I0 and I are the initial and final intensities, d is distance >>> and alpha is freq dependent. How is alpha found? >>> Thanks >>> Hardy >> Inverse Square Law, General >> http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html >> >> "Being strictly geometric in its origin, the inverse square law >> applies to diverse phenomena. Point sources of gravitational force, >> electric field, light, sound or radiation obey the inverse square >> law. >> >> Attenuation (scattering and absorption) may be factors in light, >> sound or radiation. >> http://en.wikipedia.org/wiki/Attenuation > > Yes thanks, I saw that web page when I searched but it looked like a > basic Physics page - it had no info on frequency. If you look at it it > appears as if low and high frequencies behave the same - they don't. > eg microwaves may well follow an inverse square law but they won't > travel as far as an 100MHz signal.
Search for "ionospheric propagation", "e layer", and "skip" to see why. Jerry -- Engineering is the art of making what you want from things you can get. &macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;
On 21 Aug, 23:57, HardySpicer <gyansor...@gmail.com> wrote:
> We are often told that sound intensity (I assume Power) goes down as > the inverse square of distance. However, I believe this is also > frequency dependent (as with e/m waves). What is the equation for a > sound source received at a distance d with frequency f say? I read > somewhere that low frequency sound (say 50 Hz or so) will travel vast > distances and is also humidity and temperature dependent. It mus be > something like > > I=I0.exp(-alpha.d) > > where I0 and I are the initial and final intensities, d is distance > and alpha is freq dependent. How is alpha found?
You aren't completely right but you aren't completely wrong either. Acoustics theory separate the attenuation according to the main cause. Purely geometric factors are modeled as a 1/R^2 term for spherical attenuation. But that does not account for internal friction to the material. The internal friction of the material shows up as a exp(alpha*R/lambda) where lambda is the wavelength. The friction term is frequency dependent in that lambda varies with frequancey, but also because different attenuation mechanisms dominate at different scales. Rune
HardySpicer wrote:
> We are often told that sound intensity (I assume Power) goes down as > the inverse square of distance. However, I believe this is also > frequency dependent (as with e/m waves). What is the equation for a > sound source received at a distance d with frequency f say? I read > somewhere that low frequency sound (say 50 Hz or so) will travel vast > distances and is also humidity and temperature dependent. It mus be > something like > > I=I0.exp(-alpha.d) > > where I0 and I are the initial and final intensities, d is distance > and alpha is freq dependent. How is alpha found?
The equation you have is for weakly-scattering situations. The attentuation 'alpha' (in optics the equation is Beer's law and alpha is the optical density) is generally found by direct measurement. -- Andrew Resnick, Ph.D. Department of Physiology and Biophysics Case Western Reserve University