Doppler Effect (Sound) - Source moving away from the Observer

Click For Summary

Homework Help Overview

The discussion revolves around a problem related to the Doppler effect for sound, specifically involving a moving sound source and an observer on the ground. The original poster presents a mathematical equation that relates the time of sound emission and reception, seeking assistance in understanding and solving the problem.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the times of sound emission and reception, questioning the validity of using small angle approximations. There are discussions about the implications of relativistic effects and the consistency of the speed of sound across different observers. Some participants suggest drawing diagrams and assigning numerical values to clarify the problem.

Discussion Status

The discussion is ongoing, with participants providing hints and guidance without reaching a consensus. Some have made progress in their understanding and calculations, while others continue to seek clarification on specific aspects of the problem.

Contextual Notes

Participants note the complexity of the problem and the potential vagueness in the formulation of the equation provided. There is an acknowledgment of the challenge in relating the variables involved, particularly in a relativistic context.

Armenio
Messages
4
Reaction score
0
Hi! I was doing some exercises about the doppler effect on sound until I found this problem that I can't find the solution!

"A source of sound of frequency f0 moves horizontally at constant speed u in the x direction at a distance h above the ground. An observer is situated on the ground at the point x=0 (the source passes over this point at t=0).
Show that the signal received at any time Tr at the ground was emitted by the source at an early time Ts , such that:

[1-(u/v)2]*Ts=Tr-(1/v)√(h2*[1-(u/v)2]+u2*Tr2)

where v is the speed of the sound."

Can someone please help me and explain this exercise to me? I have been trying to solve it for 48 hours and I just can't! -.-

Thank you!
 
Physics news on Phys.org
welcome to physicsforums :) Interesting problem. Where are you having difficulties? In this forum, they have a strong policy of homework helping, so we need some more information on what you have tried so far, otherwise I don't really know how to help. For example, I'm guessing that you know the answer for the problem if the source is moving exactly away from the observer? Think about how this problem is different to that problem.
 
The source at a time t is u*t away from the source at x=0 (t=0).
The distance from the source to the observer at any given t is d=sqrt(h^2+u^2*t^2).
And then I started to work with tetas and angles, but I don't know if that is correct, because I'm using small angles aproximation.
 
you should be able to do the exercise without small angle approximation. Also, this problem is a bit less straightforward than I first thought. It seems like they want you to assume that the speed of sound is the same according to all observers. Keep this in mind, and try to relate their equation to a relativistic transformation of variables. (remember Tr and Ts are times according to someone, they are not absolute, since this problem is relativistic). Also, are you sure that in the equation
[1-(u/v)2]*Ts=Tr-(1/v)√(h2*[1-(u/v)2]+u2*Tr2)
the last term is Tr2 ? It would make more sense to me if it was Ts2, I'm not sure though. This problem is a bit vague, I am not surprised that you have been working on it for a while.
 
Let p be the position of the source at time Ts. Let Δt be the time interval it takes the sound to travel from p to the observer. How are Ts, Δt, and Tr related? How can you express Δt in terms of h, u, Ts, and v? (Use your expression for d.) There's no need to use a small angle approximation.
 
Even my mechanics teacher couldn't solve the problem immediatly (I'm still waiting for an e-mail from him with some hints).

BruceW said:
you should be able to do the exercise without small angle approximation. Also, this problem is a bit less straightforward than I first thought. It seems like they want you to assume that the speed of sound is the same according to all observers. Keep this in mind, and try to relate their equation to a relativistic transformation of variables. (remember Tr and Ts are times according to someone, they are not absolute, since this problem is relativistic). Also, are you sure that in the equation
[1-(u/v)2]*Ts=Tr-(1/v)√(h2*[1-(u/v)2]+u2*Tr2)
the last term is Tr2 ? It would make more sense to me if it was Ts2, I'm not sure though. This problem is a bit vague, I am not surprised that you have been working on it for a while.

Yeah, I know. I tought the same thing but the equation is correct.
I have made some progress and I found out that:

Ts=Tr-(√(h2+u2*Ts2)/v)

I'm still working with angles and have found some curious observations.
I think I'm getting closer but I really don't know how to get to the term (1-[u/v]2)!
 
To verify your equation, you might consider drawing a diagram, assigning some numbers to the problem and then see if the answer works out. For example, let h = say 1000m, let v = 100 m/s, speed of sound 340 m/s. Assume you heard the sound at t = 5 seconds, what would Ts be?
 
Armenio said:
I have made some progress and I found out that:

Ts=Tr-(√(h2+u2*Ts2)/v)

I'm still working with angles and have found some curious observations.
I think I'm getting closer but I really don't know how to get to the term (1-[u/v]2)!

This looks good. You just need to solve for Ts. Isolate the square root on one side of the equation and then square both sides. You'll get a quadratic equation for Ts.
 
TSny said:
This looks good. You just need to solve for Ts. Isolate the square root on one side of the equation and then square both sides. You'll get a quadratic equation for Ts.

Ahahahaha of course!

You are a genius!

I've finally made the exercise and I've sent an e-mail to my teacher to teach him how to do it too.

Thank you all!
 

Similar threads

Range of frequency heard by observer related to Doppler effect
  • · Replies 8 ·
Replies
8
Views
1K
Speed of moth related to Doppler Effect
  • · Replies 8 ·
Replies
8
Views
1K
Changing of frequencies in the Doppler effect
  • · Replies 3 ·
Replies
3
Views
1K
Understanding the Doppler Effect: Solving the Bat Problem
  • · Replies 1 ·
Replies
1
Views
4K
How do you calculate wind speed using the Doppler effect?
  • · Replies 4 ·
Replies
4
Views
3K
Speed of a star in Special Relativity
  • · Replies 6 ·
Replies
6
Views
1K
Problem on Doppler effect and sound level
  • · Replies 1 ·
Replies
1
Views
2K
Spring and Microphone (Doppler Effect...?)
  • · Replies 7 ·
Replies
7
Views
3K
Apparent wavelength in Doppler's effect
  • · Replies 7 ·
Replies
7
Views
2K
Doppler effect and beat frequency
  • · Replies 3 ·
Replies
3
Views
3K