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I'm just trying to understand this problem from a qualitative perspective. The Doppler effect is commonly explained in terms of how a siren sounds higher in pitch as it is approaching a particular observer. I understand this is because the velocity of the wave is constant and so the frequency of the waves increase as they are bunched together. What would happen if a siren was mounted on say a plane traveling at a supersonic speed? To clarify what would the observer observe/hear? Apologies if my question is not phrase very well my knowledge of physics is very rudimentary.

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The thread linked to by Nicolau is about a moving observer. This question is about a moving source. The equation given in Eudoxos's comment on the other question is the one for the moving source case, so it would actually be more relevant here. –  Ben Crowell Apr 21 '13 at 2:29
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The first image shows an object traveling at Mach 1 ($v=c$). The second one shows the object traveling at some supersonic velocity ($v>c$). For both the cases, the longitudinal pressure waves pile up. Say the observer is standing in the ground and the object is traveling at $c$. The observer can't hear the pitch of sound because, the waves reach him all at once and hence, he'd hear a loud "bash". The most necessary thing is that he had to wait until the source arrives. When the source is directly overhead, he hears the shock waves.

When the object breaks the sound barrier (supersonic), it's somewhat worse. The same loud "thump" is produced here. But, the observer would notice a delay in sound (i.e) he has to wait for the shock waves to reach him. There's also this Mach cone produced by these waves since the waves group so fast behind the object. And so, there's a region of high pressure at first followed by a low pressure zone. Thus, if the object passes by in some comparable distance, it makes a lot of disturbance, "breaking things", etc...

The comic thing is, for someone inside the aircraft, he can still speak with his partner, can hear the bump of a ball on the plane, etc. The problem is only for the distant observer who suffers...

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From the supersonic image it seems that an observer standing just below the line of motion would first hear the most recent sound waves and after that the less recent waves. Does that mean he would hear the sound in reverse? –  Bart Arondson Apr 23 '13 at 22:38
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@BartArondson: Hi Bart. To answer your question, No & Yes. All wavefronts would reach his ears at more or less the same time (to a human observer, the different between the pitch - he can't notice it due to the big numbers in velocity). That's why I mentioned that an observer would hear a "thump" instead of "pitch". But, if the receiver is so sensitive (i.e - it can differentiate sounds with some slow motion) and placed along the path of the source, then you're absolutely right..! The recent wavefronts would reach him first ;-) –  Waffle's Crazy Peanut Apr 24 '13 at 5:11
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Someone standing on the ground would here a sonic boom. The sound would travel out from the plane as a coherent wave front, all the peaks will be in the same place traveling at the speed of sound (look at a picture on wiki, http://en.wikipedia.org/wiki/Sonic_boom) and will sound like an instant boom. I am not entirely sure what the pilot would hear , my guess is that it would be silent to him. I could be wrong.

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Re your last line... Everything in the plane just goes on. For example, take some passenger aircraft. If someone is speaking to someone, they both still hear what they're speaking to each other ;-) –  Waffle's Crazy Peanut Apr 21 '13 at 3:36
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