Undergrad How Does Acceleration Affect the Doppler Effect in Moving Sound Emitters?

[shawn9521]

Let's say you have a sound emitter and receiver a fixed distance apart on a moving object but open to the air, such as on the hood of a car. The emitter is near where the windshield wipers are, and the receiver is closer to the grill. They are in aligned along middle of the car, longitudinally. I understand that if the emitter outputs a constant frequency signal, the receiver will hear that same frequency no matter what fixed speed the car is traveling at.

My question is, what about during acceleration? At any point in time, the receiver is hearing the output from the emitter x time in the past because the sound has to travel the distance they are apart. So if you are at rest and you slam on the accelerator, the receiver will still be seeing the waves from the "stationary" emitter for x time while moving at a higher speed, therefore creating a Doppler effect. Is this thinking correct? Thanks in advance!

 

[davenn]

My question is, what about during acceleration? At any point in time, the receiver is hearing the output from the emitter x time in the past because the sound has to travel the distance they are apart. So if you are at rest and you slam on the accelerator, the receiver will still be seeing the waves from the "stationary" emitter for x time while moving at a higher speed, therefore creating a Doppler effect. Is this thinking correct? Thanks in advance!

the emitter and receiver are the same distance apart regardless of if the car is moving or standing still
and they are both moving together at the same speed/velocity/acceleration ( take your pick) with reference to the car

therefore there will be no Doppler effect between themDave

 

[Ibix]

Let's say you have a sound emitter and receiver a fixed distance apart on a moving object but open to the air, such as on the hood of a car. The emitter is near where the windshield wipers are, and the receiver is closer to the grill. They are in aligned along middle of the car, longitudinally. I understand that if the emitter outputs a constant frequency signal, the receiver will hear that same frequency no matter what fixed speed the car is traveling at.

There are significant practical problems with such a setup. The airflow over the car is going to mess with the propagation of the sound, and that's going to make the problem more complex than a naive Doppler analysis that assumes that the air is largely undisturbed. There's a featured thread recently on a related topic, that might be of interest.

A naive Doppler analysis would suggest that you can use this device as an airspeed meter. When traveling at constant speed the emitted and detected frequencies and wavelengths must be the same, but these will multiply together to give a speed that depends on the speed you are doing relative to the air.

I'm not sure what happens in the case where you take airflow over the car into account. I suspect you can still use this as an airspeed meter, but you'll need to know about the airflow over the car, and you'll need to talk to an engineer about that... Overall, I think it would be easier to stick with a pitot tube.

My question is, what about during acceleration? At any point in time, the receiver is hearing the output from the emitter x time in the past because the sound has to travel the distance they are apart. So if you are at rest and you slam on the accelerator, the receiver will still be seeing the waves from the "stationary" emitter for x time while moving at a higher speed, therefore creating a Doppler effect. Is this thinking correct? Thanks in advance!

Assuming you can use the device as an airspeed meter, you can use it as an accelerometer.

 

[Ibix]

the emitter and receiver are the same distance apart regardless of if the car is moving or standing still
and they are both moving together at the same speed/velocity/acceleration ( take your pick) with reference to the car

therefore there will be no Doppler effect between them

I'm not sure this is correct. Imagine the car traveling at the speed of sound (and somehow not messing up the airflow around it. The pulses would never reach the receiver - the wavelength would be zero and the frequency infinite.

Obviously that's a silly example, but I think it illustrates a general point that I need pen and paper to figure out formally...

 

[davenn]

I'm not sure this is correct. Imagine the car traveling at the speed of sound (and somehow not messing up the airflow around it. The pulses would never reach the receiver - the wavelength would be zero and the frequency infinite.

it is only traveling at the speed of sound relative to a fixed object not connected to the car !

Since the sound source and receiver are attached to the car, they and the car are motionless in their reference frame

 

[davenn]

if you are standing in a train carriage talking to some one at the other end of the carriage
there is no Doppler effect between you and the other person regardless of how fast the train is moving
as you are all moving in the same frame of reference

 

[Ibix]

Yes, but inside the train carriage you are pulling the air along with you. My understanding of the device he's proposing is that it is mounted on the outside of the car, so moving with respect to the air. If I've misunderstood and it's mounted on the inside, then I agree with you.

 

[davenn]

Yes, but inside the train carriage you are pulling the air along with you. My understanding of the device he's proposing is that it is mounted on the outside of the car, so moving with respect to the air. If I've misunderstood and it's mounted on the inside, then I agree with you.

Yes, I was, in those comments, initially working on a static air situation.

OK so as in the OP, the air is flowing from the receiver towards the source.
NOTE we are NOT dealing with a Doppler situation that is a whole different ball game., as that deals with a moving source relative to a stationary source.

here we are just dealing with the effect of the airflow over the bonnet of the car in the region between the source and receiver.
Wouldn't any air velocity towards the source just be subtracted from the speed of sound in air ?
if that is the case then I think the only time sound wouldn't be heard at the receiver may be if the airspeed is mach1 or higher ?

I'm open to corrections

Dave

 

[Ibix]

I agree with your analysis. The received frequency is always the same (at least while the car travels at constant speed), but the wavelength and speed of sound vary as a function of the airspeed as you say.

I'd argue that the changed wavelength means that the Doppler effect is involved, but I'm nitpicking terminology, not physics.

I think it bears repeating that this analysis is assuming that the car is moving through the air without disturbing it. I don't think that's a valid approximation in this application, and I'm not sure what a real version of this device would do. Airflow over a vehicle is a complicated topic and the details of it will be critical to what (if anything) this device measures.