Doppler Effect Stationary Source/Observer on a Spring

In summary, the problem involves a microphone attached to a spring that is vibrating in simple harmonic motion with a period of 2.20 s. The microphone is detecting sound from a stationary source with a frequency of 540 Hz, and the difference between the maximum and minimum sound frequencies detected is 1.83 Hz. Using the equation for the Doppler effect, the difference in frequencies can be used to find the velocity of the microphone. Then, by differentiating the equation for position in SHM, the amplitude can be calculated using the maximum velocity.
  • #1
jamiewilliams
11
0

Homework Statement


A microphone is attached to a spring that is suspended from the ceiling. Directly below on the floor is a stationary 540-Hz source of sound. The microphone vibrates up and down in simple harmonic motion with a period of 2.20 s. The difference between the maximum and minimum sound frequencies detected by the microphone is 1.83 Hz. Ignoring any reflections of sound in the room and using 343 m/s for the speed of sound, determine the amplitude (in m) of the simple harmonic motion.

Homework Equations


f(obs)= f(source) (1-(v(obs)/v))
ω=2[itex]\pi[/itex]/T
v(max)=Aω

The Attempt at a Solution


When I inquired about help I was told that I need to combine the equations for the max and min frequencies to get the maximum velocity, but I can't figure out how to do that. I am also not sure what to do with the difference of the max and min frequencies that was given in the problem. I have figured the value of ω to be 2.86 rad/s.

I think I would use the equation v(max)=Aω once I had the max velocity to get the amplitude.

I feel like this problem should be easier but I just can't figure it out!
 
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  • #2
combine the equations for the max and min frequencies
Write your dopplar equation twice, once with positive Vo and again with negative Vo. One gives the maximum frequency observed, the other the minimum, so the difference between the two is your 1.83 Hz. That's your clue to subtract the two equations. I think you will be able to get Vo out of that.

Regarding the amplitude, I wonder if you have an equation something like
x = A*sin(ωt) for the position as a function of time. And can differentiate it with respect to time to get a similar equation for the velocity. The two of them would constitute a relationship between the amplitude and the maximum velocity.
 
  • #3
Thank you so much! I just subtracted the min frequency from the max and set it equal to 1.83 Hz.

I did, however, use the v(max)=Aω to find the amplitude, but versus time the other equation would have worked better.

:)
 
  • #4
Most welcome!
v(max)=Aω comes from differentiating x = A*sin(ωt).
 
  • #5
Didn't even notice that, I haven't thought about differentiation (or calculus) in a few semesters :)
 

1. What is the Doppler Effect?

The Doppler Effect is the change in frequency or wavelength of a wave as it moves towards or away from an observer. This effect is observed in sound waves, light waves, and other types of waves.

2. What is a stationary source/observer on a spring?

A stationary source/observer on a spring is a physical model used to demonstrate the Doppler Effect. It consists of a source of waves attached to a spring, and an observer that is stationary but can move along the spring's axis.

3. How does the Doppler Effect change with a stationary source/observer on a spring?

The Doppler Effect is amplified in a stationary source/observer on a spring model because the movement of the spring causes the source and observer to be constantly changing their distance from each other. This results in a more noticeable change in frequency or wavelength of the wave.

4. How is the Doppler Effect calculated in a stationary source/observer on a spring model?

The Doppler Effect in a stationary source/observer on a spring is calculated using the equation: Δf/f = v/c, where Δf is the change in frequency, f is the original frequency, v is the velocity of the spring, and c is the speed of the wave.

5. What are some real-world applications of the Doppler Effect with a stationary source/observer on a spring?

The Doppler Effect with a stationary source/observer on a spring can be applied in various fields such as acoustics, astronomy, and meteorology. It is used to study the motion and properties of stars, galaxies, and other celestial objects. It is also used in weather radar to detect the speed and direction of storms. In acoustics, it is used to measure the speed of moving objects, such as vehicles, and in medical imaging techniques like ultrasound.

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