# Sound Intensity

Started by 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.
&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;
```
```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,
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,
>      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!)

```
```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,
>>      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)
http://www.mhhe.com/physsci/astronomy/fix/student/chapter6/06f28.html

```
```"HardySpicer" <gyansorova@gmail.com> wrote in message
> 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.

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,
>>      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
```