Calculating Doppler Shift from Ambulance Movement

In summary, the conversation discusses using the given information to compute the exact doppler shift of an ambulance passing by at a distance of 4m with a velocity of 10m/s^2, while the observer has a 2.2 GHz radar. The equation R'=10x/R is derived, but further information is needed to determine the values of x and r and ultimately solve for the acceleration of the ambulance.
  • #1
jamcintyre1
6
0
1. Homework Statement
You are standing on side of road and ambulance drives by. Smallest distance between you and ambulance is 4m. Ambulance v=10m/s^2. You have 2.2 GHz radar. Ambulance travels 100m with center of straight line directly across from you.
Compute exact doppler shift by taking derivative of range vs time equation.
Give ambulance acceleration


2. Homework Equations
R'=|V_T|cos(theta)
f_d=-2R'/lambda


3. The Attempt at a Solution
R^2=x^2+y^2 (x and y axes, x-axis defined as direction ambulance is driving)
implicitly derive
2RR'=2xdx/dt+2ydy/dt
y=4
2RR'=2xdx/dt+8dy/dt
dy/dt=0
2RR'=2xdx/dt
dx/dt=10
2RR'=20x
R'=10x/R

Now what?
 
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  • #2
OK so far.

What is x(t)? You need to define a relationship between x and t and stick to it.
What is r(x,y)? (Use r, not R. R implies a constant).
Then come up with dr/dt in terms of v, t and y.
 

Related to Calculating Doppler Shift from Ambulance Movement

Question 1: What is Doppler shift and how does it relate to ambulance movement?

Doppler shift is the change in frequency or wavelength of a wave as it moves towards or away from an observer. In the case of ambulance movement, the siren on the ambulance emits sound waves that are affected by the movement of the ambulance. This results in a change in frequency, which is known as Doppler shift.

Question 2: How is Doppler shift calculated from ambulance movement?

To calculate Doppler shift from ambulance movement, you can use the formula: Δf = f * v/c, where Δf is the change in frequency, f is the original frequency of the sound waves, v is the velocity of the ambulance, and c is the speed of sound. This formula takes into account the relative motion between the observer and the source of the sound waves.

Question 3: What factors can affect the calculation of Doppler shift from ambulance movement?

The calculation of Doppler shift from ambulance movement can be affected by several factors, including the velocity of the ambulance, the frequency of the siren, the distance between the observer and the ambulance, and the speed of sound in the medium (which can vary depending on factors such as temperature and altitude).

Question 4: How is Doppler shift used in real-life situations involving ambulance movement?

Doppler shift is commonly used in real-life situations involving ambulance movement to help determine the direction and speed of the ambulance. This information can be crucial for emergency responders to navigate through traffic and arrive at the scene of an emergency as quickly as possible.

Question 5: Are there any limitations to using Doppler shift for calculating ambulance movement?

While Doppler shift can provide useful information about ambulance movement, it is important to keep in mind that it is only accurate if the ambulance is moving in a straight line towards or away from the observer. If the ambulance is turning or changing speed, the calculation of Doppler shift may not accurately reflect its movement.

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