MadSci Network: Physics Query:

### Re: The speed of sound in front of a moving source

Date: Fri Jul 31 10:17:43 2009
Posted By: Rob Fatland, Staff, Research and Education, Freelance Science Educator
Area of science: Physics
ID: 1248001558.Ph
Message:

For this answer please understand: A domino if you are not familiar with it is a little wooden or plastic (usually) tile usually about 3 cm by 6 cm by .75 cm thick. These can be lined up on edge in a row: |||||||||||| and the first one can be pushed over: /||||||||||| and this causes the next to fall and so on: //////|||||||| until eventually they have all fallen over: //////////////////_.

This explanation: I have broken it into 3 parts.

Sound propagates faster than your (typical) moving object and is the result of typically hundreds to thousands of "pushes" or oscillations per second. Sound is also a decoupled phenomenon: it is the result of many independent air molecules bumping into one another in a coherent way due to these pressure oscillations at the source.

To set this up in what I hope is an instructive scale analogy: Part 1 is to consider a snail that knocks over the first of a series of dominoes. The dominoes are like air molecules. The chain of dominoes moves away from the snail very fast (from the snail's point of view). The dominoes as they fall don't "know" about the snail; each domino just knows it got bumped into by another domino and that it is falling over to bump into a different domino.

That's part 1. Part 2 is that perceived sound is actually many domino falls or ripples in rapid succession. So imagine that each domino in your chain of dominoes can instantly "stand up again" after falling over, perhaps by being attached somewhere by a rubber band. This is getting closer to the case of air molecules: They are still there and can continue bouncing into one another. Now your snail knocks over the first domino. That sets off a ripple of falling dominoes but that first domino bounces right back, as do the others. The snail waits a little bit and knocks the first domino over again. The same thing happens: The dominoes fall and stand back again. Many ripples. The snail does this for awhile always waiting the same amount of time before the next push. The successive ripples of falling dominoes has a frequency, which in terms of sound is a pitch that we hear. If the snail starts pushing the first domino over more frequently (waits less time between pushes), by analogy this is a sound wave of a higher frequency so the perceived pitch goes up.

Notice that if the dominoes were all stacked together, physically touching one another face to face, and if the speed of sound were just the last domino moving forwards (rather than repeated waves of falling dominoes) then the snail's speed *would* determine the speed of sound. The snail would push all the dominoes at once and the end domino would move just as fast as the snail. But this is not how sound works in air.

Now for part 3 let's abandon the snails and dominoes in favor of a siren on an ambulance. The ambulance is rushing along at 50 km / hour and the siren is going off very loudly. This siren is vibrating the air at say 2000 times per second, so at the speed of sound (about 300 meters per second) these pressure waves are spreading out like ripples on a pond, 2000 ripples per second from the point of view of the ambulance driver. These ripples travel by means of air molecules bouncing into one another; but each air molecule doesn't know about the ambulance. It only knows that it got bumped into again and again at some frequency, and that it in turn is bumping into other air molecules at the same frequency. All together all of these jiggling air molecules create little pressure waves spaced about 15 cm apart (300 meters per second divided by 2000 waves per second).

Now suppose you are standing on the sidewalk up ahead of the ambulance. The ambulance is moving at 50 km per hour (4 meters per second) towards you. So each successive pressure wave in the direction the ambulance is moving is created about 2 millimeters closer to you than the previous one (compared to if the ambulance were not moving). So the pressure waves are hitting your ears closer together in time than if the ambulance were not moving. This causes the perceived frequency of the ambulance to become higher. So the speed of sound does not change but the frequency of the siren does ahead of the ambulance. As the ambulance passes by it is now getting further away and the effect is reversed: The frequency of pressure waves drops and the pitch of the siren becomes lower behind the ambulance. This curious change in pitch as the ambulance passes by is often referred to as the Doppler effect.

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