# The Naked Scientists Forum

### Author Topic: Can you determine the speed of a passing car with a sound recording?  (Read 8502 times)

#### Karsten

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##### Can you determine the speed of a passing car with a sound recording?
« on: 06/08/2009 02:08:46 »
So, there is the Doppler effect and I want to use it. Can I record the sound of a passing car and determine the frequencies of approaching and leaving car by matching with musical notes (which equal frequencies) and then just calculate the speed of the car on paper? If yes, please guide me through the process of calculating this. I also need to know which note equals which frequency. Maybe there is a online synthesizer that allows me to create sounds with my keyboard and tells me exactly what frequency they are. Then I could match the sounds to the frequency. The frequency matching I am less concerned with. Any music teacher can help me with this, but the math???

Anyone?

#### RD

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##### Can you determine the speed of a passing car with a sound recording?
« Reply #1 on: 06/08/2009 17:00:12 »
Can I record the sound of a passing car and determine the frequencies of approaching and leaving car by matching with musical notes (which equal frequencies) and then just calculate the speed of the car on paper?

A good Doppler effect sound recording here ... http://www.freesound.org/samplesViewSingle.php?id=28426
[press the play triangle on the top left of the waveform to hear it].

A Digital Audio Workstations (DAWs) like the free Audacity have a frequency analysis feature: it can show you a graph of the frequency content of a selected part of a sound recording.

Doppler maths ... http://en.wikipedia.org/wiki/Doppler_effect
« Last Edit: 06/08/2009 17:23:19 by RD »

#### RD

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##### Can you determine the speed of a passing car with a sound recording?
« Reply #2 on: 07/08/2009 04:37:42 »
The frequency content of the first note of this police siren approaching is in red, receding in blue ...

The fundamental frequency of the first note of the the siren, ("nee" of "nee-naw"), is 503Hz approaching and 460Hz receding.

Using the Doppler formula here I calculate the police car is doing 14.4ms-1, that's about 32 mph in old money.
« Last Edit: 07/08/2009 04:59:50 by RD »

#### lyner

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##### Can you determine the speed of a passing car with a sound recording?
« Reply #3 on: 07/08/2009 10:21:46 »
To calculate the speed exactly, you also needto know the path that the car is taking, relative to you. Doppler will tell you only the rate of change of distance FROM YOU. you need to include the geometry of the situation. The max Doppler effect will be when the car goes directly past (through) you. At a large distance from the road there is less effect.  Because there is a limit to how far away the car can actually heard, you need to take this into account.
Perfectly doable but the sums still have to be done.

#### Karsten

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##### Can you determine the speed of a passing car with a sound recording?
« Reply #4 on: 07/08/2009 13:50:16 »
To calculate the speed exactly, you also needto know the path that the car is taking, relative to you. Doppler will tell you only the rate of change of distance FROM YOU. you need to include the geometry of the situation. The max Doppler effect will be when the car goes directly past (through) you. At a large distance from the road there is less effect.  Because there is a limit to how far away the car can actually heard, you need to take this into account.
Perfectly doable but the sums still have to be done.

Yes, I guess it would be best to have the microphone right ON THE ROAD to get the best measurement. At least, the closer the better. If I want to avoid trigonometry.

Audacity is a good tip. I have it already installed.

I will need to look at the math more.

#### RD

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##### Can you determine the speed of a passing car with a sound recording?
« Reply #5 on: 07/08/2009 15:22:34 »
I assumed the police car was travelling on a straight road at a constant speed
and the microphone was on the side of this straight road, (microphone on sidewalk).

The sample points I took would have been 50-100 meters from the microphone
: far enough from the microphone to ignore trigonometry if an approximation (+/-10%) is required.
« Last Edit: 07/08/2009 17:50:06 by RD »

#### lyner

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##### Can you determine the speed of a passing car with a sound recording?
« Reply #6 on: 07/08/2009 17:45:01 »
Fairy Nuff. Nice bit of work.
I just had to point out some practicalities.
I notice the car was sticking to the speed limit!

#### RD

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##### Can you determine the speed of a passing car with a sound recording?
« Reply #7 on: 07/08/2009 17:57:05 »
I notice the car was sticking to the speed limit!

Not a typical Italian* driver then

[* The sound recording is in Rome ]
« Last Edit: 07/08/2009 18:12:06 by RD »

#### techmind

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##### Can you determine the speed of a passing car with a sound recording?
« Reply #8 on: 12/08/2009 22:35:38 »
...Can I record the sound of a passing car and determine the frequencies of approaching and leaving car ... and then just calculate the speed of the car on paper?

In principle yes, but the pre-requisite is that you need to know that the car itself is emitting the same sound on its approach and its departure. If it's an emergency vehicle with a siren, then that's a constant sound (or a constant range of tonal sweep), or if it's the car stereo turned up loud and you have perfect-pitch then that would also work. If you were relying on the engine noise then you'd require that the car is travelling at a constant speed (so the engine makes a constant-pitch hum/whine).

The frequency shift on the approach is f(heard) = f(made)*(1+v/c)
And on the departure is f(heard) = f(made)*(1-v/c)

where v is the velocity of the car and c is the speed of sound (330 metres per second = 740 mph).

There are 12 semitones in an octave (doubling of frequency), so each semitone (on an equally-tempered scale) is the 12th root of 2 fractional pitch change, ie frequency increases by 1.05946... (near enough 6%) going from one semitone to the next.

Since the before and after pitch-change is 1+2*v/c, a pitch change of one semitone would be equivalent to a speed of 3% of the speed of sound, ie 3% of 740mph ie 22mph.
A change of 2 semitones would be 44mph
3 semitones 66mph
4 semitones 88mph
5 semitones 110mph etc.
« Last Edit: 12/08/2009 22:44:15 by techmind »

#### nicephotog

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##### Can you determine the speed of a passing car with a sound recording?
« Reply #9 on: 01/09/2009 15:13:29 »
Barometeric and air pressure may hold a clue to that apart the general frequencies emitted from the vehicle model by its own properties.
That's how air speed is measured in part(and apart Doppler).
Isn't that what they thought was possibley the problem with the air liner went down near argentina a few months back.

#### teragram

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##### Can you determine the speed of a passing car with a sound recording?
« Reply #10 on: 01/09/2009 17:09:00 »
I also need to know which note equals which frequency.

Frequencies of notes based on treble A as 440Hz (concert pitch) are:-
C        261.6
C sharp  277.2
D        293.7
D sharp  311.1
E        329.6
F        349.2
F sharp  370.0
G        392.0
G sharp  415.3
A        440.0
A sharp  466.2
B        493.9
C        523.2 (next octave)

I'm not much of a musician, I just happen to have a book with the info in, (Open University, "Science Data Book")

#### Karsten

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##### Can you determine the speed of a passing car with a sound recording?
« Reply #11 on: 02/09/2009 12:38:15 »
I also need to know which note equals which frequency.

Frequencies of notes based on treble A as 440Hz (concert pitch) are:-
C        261.6
C sharp  277.2
D        293.7
D sharp  311.1
E        329.6
F        349.2
F sharp  370.0
G        392.0
G sharp  415.3
A        440.0
A sharp  466.2
B        493.9
C        523.2 (next octave)

I'm not much of a musician, I just happen to have a book with the info in, (Open University, "Science Data Book")
Thanks!

#### teragram

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##### Can you determine the speed of a passing car with a sound recording?
« Reply #12 on: 02/09/2009 16:04:50 »
Karsten: You're more than welcome!

#### The Naked Scientists Forum

##### Can you determine the speed of a passing car with a sound recording?
« Reply #12 on: 02/09/2009 16:04:50 »