The Doppler effect’s contribution to the propagation of sound on a windy day



Why can the wind transmit the noise so effectively in the direction of wind and mitigate it in the opposite direction ?


In the preferential travel of sound in the direction of the wind and in its poor travel in the opposite direction we certainly have cumulative effects. This article shows that one of them is a double Doppler effect or rather a double ‘dopplerization’ combined with a frequency dependent attenuation.


(physics, acoustics, wind, sound, speed, trains, Doppler effect, French humor)
This original article was written in french for Knol in December 2008 and translated to english in january 2009, many thanks to BJ for his help. Many people are surprised that the wind (which speed is on the order of 10 m/sec, often much less) may change the range of sound that propagates much faster ( speed on the order of 350 m /sec).  Some people have not experimented this personally and comically try to verify on the internet the truth of this statement, which is well-known to people living in the countryside, hunters, etc.

The Doppler effect

The Doppler effect is usually presented as a phenomenon linked to a change of distance between a source and a receiver.

Appreciate this very surrealistic drawing from http://www.fygo.dk/files/ukursus/Ultrasound%20Doppler.pdf
(The smoke from the locomotive, which is inhaled by the musician, is not shown … more seriously, it would be interesting to know what the locomotive drive hear?)

For example, the entry on the Doppler effect in Wikipedia (2008) states that:

The Doppler effect or D. shift …… is the change in frequency and wavelength of a wave for an observer moving relative to the source of the waves.

Now have a look at this other drawing,

extracted from “waves_doppler.ppt”, a presentation from http://www.csulb.edu (California State University at Long Beach) through the link  http://www.filestube.com/e345996af8ec0b9f03e9/go.html.

the author seems to have been Igor Glozman, a professor now at Higline Community College, Des Moines, WA, USA (?)


This page overlooks the fact that the medium (the air) itself can move too [1]  … but it is already an improvement over 90% of presentations which always talk about the ambulance that passes by us (like in the left drawing), forgetting the stopped ambulance, with the siren blaring (like in the right drawing) at the side of the road when we are passing by.  You could say that ambulances do not turn on their siren when stopped, but then I would say: Fool ! This is an example in which there is no ambulance in fact!   It was given here to understand the Doppler effect…).
So this drawing has the bonus to show that the medium can be still relative to the source or still relative to the listener. If on the listener side the Doppler shift  is similar, physically the wave train is distorted only if the emitter is moving relative to the medium (the second figure). Otherwise,  a deformation of the wave train cannot be represented (whence the third figure).

In the previous schemes, the “Dopplerization” occurs only once, at the sender’s place or at the receiver’s place as appropriate, in fact at the place where there is a differencial in speed.

But what do we call “Dopplerization”?  First we must distinguish it completely from the effect usually described – the frequency change observed by a person or an appliance. We call Dopplerization the “distortion” of the wave field (effective, real, and active and occurring when there is a difference in speed between the transmitter and the air) or virtual and passive (speed differential between the receiver and air). In both cases, this Dopplerization changes a concentric field to a non-concentric field or conversely, or even between two non-concentric fields:

Real Dopplerization: The wave field is distorted. CAUTION: This pattern, which usually represents a moving sound source in fixed air (but may also represent a stationary source in moving air) does not mean that the wave will propagate slower to the right (the wave propagrates at the same speed in all directions). It does not either represent the range of the waves. This diagram only shows that the wavelengths are packed on one side and stretched on the other. Please do not look at this figure any longer, I mean it! I now count to three and you will wake up, pick up your clothes, and return to your seat…

In short, the traditional ways of presenting the Doppler effect describes the outcome of single Dopplerisation and not its operation (with its two aspects), and tends to overlook the possiblity that the  phenomenon could be involved in situations where the distance between transmitter and receiver does not change, a possibility that we will now develop.

To be fair, this matter happened to be briefly discussed in a forum that we found by chance during the writing of this article [2]. Of course, I thank you for reporting any article that could address the issue (a forum in english was  later discovered as well. [3])

The propagation of sound and atmospheric refraction

Articles studying the propagation of sound (often in a noise control perspective) [4] between a stationary source and a stationary receiver evidently include wind as a factor which could change the propagation of the sound. They focus on the refraction of sound waves within a wind gradient (The temperature gradient is also sometimes included) as the main cause of enhanced propagation in the direction of the wind and the poor propagation against the wind.  A demonstration:

In this figure, the wind is weaker near the ground AND/OR the air is colder near the ground (common in the night/morning : temperature inversion)

In this figure, the wind is AGAIN weaker near the ground AND/OR the temperature is higher there (usual situation during the day)

The wind is weaker on the ground than in altitude because of friction. This induces a gradient of intensity in the wind between the ground and a certain altitude, which is well known to balloonists and aviators.  (They also know about a gradient in wind direction, because faster moving air masses are subject to a greater Coriolis force.  Thus a slow-moving particle of air is deflected less by the gradient force, but this is irrelevant to us.)

In the gradient of intensity sounds are moving at different speeds in different directions wich give birth to refraction:

Upwind, the speed of sound waves relative to the source increases with altitude as the wind speed increases. Downwind, the speed of sound waves defined in the same way decreases with height.

Refraction always bends the waves toward the direction of a lower propagation speed so:

The sound energy is deflected toward the ground downwind, while it is deflected into the sky upwind.  Downstream, the sound energy remains close to the ground, upstream, it is sucked into the sky so at a certain distance horizontaly you have a “shadow” zone that the sound does not reach.

The refraction clearly explains part of the difference in transmission of sound down the wind and against the wind that we observe. For example, if you live near a road, even a slight wind may bring you the noise of the road or may hide the noise from you, depending on the direction in which it blows.

This effect also explains why the sound “carried” by the wind is able to overcome some obstacles by “jumping over”, a phenomenon early discovered by those who built the first anti-noise walls!

However, this theory has a weakness: the propagation of sound is also dependent on the nature of the “ground.”  This can be demonstrated at a lake with no wind and no waves.   Here, you can hear the noises coming from the other side, whereas if it were a field, you would certainly hear nothing !  In a normal terrain in the direction of the wind, the sound waves deflected towards the ground should be muffled and absorbed, and it is not clear how these deflected waves could recover to keep on going in the good direction, i.e., the horizontal direction. In fact, the refraction theory better explains the poorer sound propagation against the wind than the good propagation in the direction of the wind.

A complementary theory: the double dopplerisation

In our model the gradient wind is not necessary. The wind is supposed homogeneous, but the presence of a gradient wind does not interfere with its operation. At the time of the emission of the sound, the sound frequencies are dopplerized by the difference in speed between the stationary emitter and the medium of propagation, air (Physically, there is no difference between this case and a mobile source in still air.  The deformation of the wave train is the same).


<<<<<<<<<<< WIND <<<<<<<<<<

In this figure, as you can see, I added the word “wind” at the bottom.  With my amendment, therefore, the black dot no longer moves to the right in the figure below. Instead, there’s wind blowing to the left.  Do you see what I mean?

People in a balloon who would be drift along the source in the flow of air could clearly hear the different characteristic effects called “the Doppler effect” before and after their passage near the emitter.
Downwind, the frequency of the sound is reduced. In contrast, the frequency increases against the wind. (the wavelength increases in the first case and it decreases in the second case.)

But upon reception by a stationay actor, be it a human or a machine, the airwaves will be redopplerized in the opposite way (or dedopplerized …), and consequently found to have the same original frequency. Therefore, there will be no “Doppler Effect” for this receiver.

So in this case there is no Doppler shift felt upon arrival but there have indeed been a double dopplerisation !

Then It is well known that attenuation of sounds is slower at low frequencies than at high frequencies. This allows the elephants (but not the mouse!) to communicate over long distances, by using infra-sound.

Therefore, sounds dopplerized to a low pitch at the time of emission will travel further than the same sound dopplerized to a higher pitch, and therefore, will be perceived at a longer distance. The site, http://www.ndt-

ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/attenuation.htm teaches us that mitigation is proportional to the square of the frequency.  By performing a simple calculation, we can calculate the difference in attenuation, over the same distance, of the same sound propagated at different frequencies.

Conclusion

Finally, we must take in account that these two effects of wind, refraction and dopplerization, combine with a third effect, little-documented (because it is considered negligible) but still real, which is the physical transport of the wave. Indeed, the sound waves are transported by air in the direction of the wind.  Therefore, travel in the right direction is shorter (in time and distance in the air) than travel in the wrong direction.

Complementary Experiments

Apart from these calculations, we can devise an experiment for assessing the contribution of the Doppler effect by eliminating the effect of refraction: just place two people, or a sound emitter and a sound receiver, sufficiently apart on a train car or on the deck of a boat in motion. Then measure the attenuation in both directions. This first experiment has the disadvantage of not suppressing the physical transport (as defined above).

So, can you devise an experiment to study the attenuation due to the double Dopplerization without transportation nor refraction?

That is the question we ask to our readers!  Thank you for offering this experiment in the comments.  Above all, thank you for submitting less than 1,000 comments per day.  That saturates Google’s servers … (solutions to come).

Annex:
In the presentation from wich I took the picture above (with the sport car and the two children) I found an interesting problem :

My correction of the problem of a crazy train with a whistler (p. 21. in the said document)

Here is the statement :
Two trains are traveling toward each other at 16 m/s relative to the ground. One train is blowing a whistle at 1320 Hz.
(a) What frequency will be heard on the other train in still air? (Assume the speed of sound in air is 343 m/s.)
(b) What frequency will be heard on the other train if the wind is blowing at 16 m/s toward the whistle and away from the listener?
(c) What frequency will be heard if the wind direction is reversed?

Personally, I am tempted to add another question : What frequency will be heard by the receiving train, once it understood that the other runs to him like crazy while whistling, and then as it begins to move backward to avoid the
collision (this new question through the three wind situations)

question (a):

Dopplerization 1 (or active)

Dopplerization 2 (or passive)


this result is the same as that calculated by our friend

Either

Question (b):

Dopplerization 1


Dopplerization 2: there is no second dopplerisation since the second train is still relative to the air! Both go at 16 m/sec toward the other train.

The frequency heard by the second driver, according to our calculation, is significantly different from that calculated by our friend Igor Glozman!

Question (c):

Dopplerization 1: there is no first dopplerisation since the first train, the emitter, is stationary relative to the air!  Both go at 16 m/sec toward the other train, receiver …

thus

Dopplerization 2


Conclusion:
Given the recognition of the intrinsic asymmetry of the two dopplerizations, as clearly highlighted in p. 12, our friend should have been surprised to find the results so symetric when the air moves, compared to when it is stationary (10 Hz more or less depending on the direction of the wind is suspicious …)

When the air is stationary, there are two Dopplerizations, and the final frequency is affected by the contributions from both. When the air is moving at the same speed as one of the two trains, one of two Dopplerizations is removed, then it is logical that the contribution from an active Dopplerization (when the source moves relative to the air ) is higher than the contribution of a passive Dopplerization, as provided on page 12:
The first raises the frequency to 1,455 Hz (5 Hz higher than the case through calm air).
The second raises the frequency up to 1443, or 7 Hz lower than the case of through calm air.

Références

  1. Hum, in fact this document is awesome but also very rough. It actually contains a reference to a moving media. Just go to page 20, where there is a Sibyllines formula. The problem is that this formula ( the author focus since the beginning of the document on the change in the observed frequency) is unable to calculate a correct answer in a case of double dopplerization with a stationary source and a stationary receiver !?! the presentation still has the merit of proposing a problem with wind and moving players … Thus, we have recalculated the problem on page 21 in the text … and we have found the results inaccurate.
  2. http://groups.google.fr/group/fr.sci.physique/browse_frm/thread/9bc68a73d25b5fc8 Wenceslas wrote:>> Why do we hear a person less where there is wind?>> Speak only when there is no wind? > This question makes me think of another: if one speaks with or againt > the wind, is he does a doppler? – Yes, logically. It was at the time of the emission that “compression” or “extension” of the wave crests. And it depends only on the relative velocity between the source and the medium itself. But the opposite happens at the place of reception. So ultimately, if the source is stationary in relation to the receiver, there is no Doppler effect.
  3. http://en.allexperts.com/q/Physics-1358/doppler-effect-1.htm (This pose the question correctly, but does it answer correctly?) http://yedda.com/questions/Doppler_effect_wind_physics_8627845471015/ ( answered negatively.) http://answers.google.com/answers/threadview/id/550444.html (links to many other references) http://encarta.msn.com/text_761560639___2/Sound.html (only talks about refraction)
  4. E. Premat – Jérôme Defrance, acoustic propagation in the external environment, Pour la Science N ° 32 – July 2001

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  1. Festival Support

    Very good article. I certainly appreciate this site. Keep writing!

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