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Thread: The speed of sound in an enclosed compartment.

  1. #1 The speed of sound in an enclosed compartment. 
    Junior Member GerryB's Avatar
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    Two observers are riding on a train traveling along a straight level section of track at the constant velocity, v. It is a windless day, so that the air/medium is at rest relative to the moving train. Relative to the train’s direction of travel one observer sits at the rear of a train car of length L, and the other observer sits at the front of the same train car. The windows and doors are closed, so the air molecules inside the train car share in the motion of the train car.

    The rear observer is holding a flashlight and a clock, the front observer has nothing. They sit facing each other then she begins their thought experiment. She flashes the light towards the other observer and starts her clock at the same moment. When the other observer sees the flash of light he yells back at her. When the sound wave of his yell reaches her she stops her clock. The light signal is effectively instantaneous over this short distance so the duration of time she measures is for the sound wave to travel at the constant velocity calong the length L to her ear. The speed of sound c is constant in that the emitter does not add any velocity to the sound wave due to the emitter‘s motion. She would then calculate the speed of the sound wave as ce = L / te, where t is the time measured inside the enclosed compartment. In this case the distance the sound wave travels is equal to L due to the forward velocity of the molecules matching the train‘s velocity. The time value measured should be as if the train were at rest.


    Next, the two observers clamber up to the roof of the same train car and take their same positions at the front and rear of the train car. She begins the same experiment that they performed earlier but now they are exposed to the stationary air with the train moving through the air molecules at the constant velocity, v. She once again flashes the light signal and at the same moment starts her clock. He yells once again when he sees the signal then she measures the time for the sound wave to reach her ear. She then calculates the speed of the sound wave as cr = L / tr, where tr is the time measured on the roof of the enclosed compartment. In this case the distance the sound wave travels is less than L due to the air molecules having zero velocity as the train plows through them at the velocity v. The time value measured should be less than if the train were at rest.


    If te does not equal tr then has she measured two different values for the speed of sound, c? Is there a difference between measuring the time within the enclosed compartment where the air molecules have the velocity of the train, and measuring the time on the outside of the train car where the air molecules have a velocity of zero?
    Last edited by GerryB; 07-06-2014 at 11:29 PM.
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  2. #2  
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    Hi Gerry B, welcome to the forum. I don't think you could conclude that the speed of sound had changed since you know you are moving relative to the medium.
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  3. #3  
    Junior Member GerryB's Avatar
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    Quote Originally Posted by Jilan View Post
    Hi Gerry B, welcome to the forum. I don't think you could conclude that the speed of sound had changed since you know you are moving relative to the medium.
    You are thinking exactly what I was thinking. I edited some additional statements to reflect just what you said. From inside the compartment the time measurement would appear as if the train were at rest. But I think the time measurement on the roof would be less due to the forward velocity of the train.

    Thanks Jilan
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  4. #4  
    KJW
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    The speed of sound relative to the air at rest is constant, so for air in relative motion, the velocity of that motion will add to the velocity of the sound in the air at rest.
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    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Junior Member GerryB's Avatar
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    I think we are mostly in agreement KJW, but it would be a subtraction inside the enclosed compartment since the observer is moving in an opposite direction to the sound wave. I am having trouble trying to figure out what the effects of the velocities of molecules are on the velocity of the propagating sound wave.
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  6. #6  
    KJW
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    Quote Originally Posted by GerryB View Post
    I think we are mostly in agreement KJW, but it would be a subtraction inside the enclosed compartment since the observer is moving in an opposite direction to the sound wave. I am having trouble trying to figure out what the effects of the velocities of molecules are on the velocity of the propagating sound wave.
    No, inside the enclosed compartment, the observer is not moving relative to the air, which is moving with the train. The motion of train relative to the tracks is irrelevant, only the motion of the air relative to the observer is relevant.
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    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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  7. #7  
    Junior Member GerryB's Avatar
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    Quote Originally Posted by KJW View Post
    No, inside the enclosed compartment, the observer is not moving relative to the air, which is moving with the train. The motion of train relative to the tracks is irrelevant, only the motion of the air relative to the observer is relevant.
    I disagree with you on that point KJW. I think that the motion of the enclosed compartment relative to the tracks is very relevant. That is why I made the post. The comparison of the time mesurement inside the enclosed compartment, and the time measurement on the roof of the enclosed compartment must mean something. Do the air moluecules belong to one reference frame or another? Are the air molecules free to move between reference frames?
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    In the closed compartment the motion of the traiin, automobile, aircraft, ship or space craft is irrelevant to what happens inside.

    Outside the relative air movement can prevent you from hearing the sound if you are going faster than the speed of sound and you are in front of the source.
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  9. #9  
    Junior Member GerryB's Avatar
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    Do the walls of the enclosed compartment establish the reference frame, or do the perpendicular coordinate axes establish the reference frame? In one case the air molecules are limited in their movements but in the other case the air molecules are free to move between two reference frames. How do we mathematically handle this?
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