Deriving Formula: f2 Frequency of Moving Object

In summary, the formula for finding the frequency of a sound made by an object moving towards or away from the listener is f2= f1(v/v-vs) or f1(v/v+vs), where f2 is the second frequency, f1 is the first frequency, v is the velocity, and vs is the velocity of the source. This formula can be derived by considering the distance between two successive crests emitted by a moving siren. The beat frequency formula is not necessary for solving this problem.
  • #1
The Tutor
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Homework Statement


This is my first post, so it might not be that great... Anyways, I need help deriving the formula. This formula is pertaining to the doppler effect, and more specifically, to find the frequency of a sound made from an object moving toward/away from you.

f2= f1(v/v-vs) or... f1(v/v+vs)

Where f2 is the second frequency, f1 is the first frequency, v is velocity, and vs is the velocity of the source.

Homework Equations



v=(lambda)(frequency) (I don't know how to make any symbols =/)
v=d/t
beat frequency= absf1-f2endabs

The Attempt at a Solution



What I did was try to make every variable a frequency, and I had no idea what to substitute in for vs...
 
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  • #2
I don't think you need the beat frequency formula.

Think about the problem like this. At a certain moment in time, a siren emits a crest (or trough; take your pick), and the energy spreads out in all directions at the same speed. After one period passes, it emits another crest, which again spreads out in all directions. If the siren's moving, this crest will be closer to the initial crest in the direction of motion and farther from it in the opposite direction. If you can find the distance between the two crests, that's your wavelength.
 
  • #3
ideasrule said:
I don't think you need the beat frequency formula.

Think about the problem like this. At a certain moment in time, a siren emits a crest (or trough; take your pick), and the energy spreads out in all directions at the same speed. After one period passes, it emits another crest, which again spreads out in all directions. If the siren's moving, this crest will be closer to the initial crest in the direction of motion and farther from it in the opposite direction. If you can find the distance between the two crests, that's your wavelength.

I think I might've worded my question wrong; I'm trying to prove the formula itself, I don't need to find the wavelength; unless that is what I am suppose to do?
 
  • #4
I don't think lambda was suppose to use in the original equation, was it? I forgot to add that part in my original question.
 

Related to Deriving Formula: f2 Frequency of Moving Object

What is the formula for calculating the frequency of a moving object?

The formula for calculating the frequency of a moving object is f2 = v/λ, where f2 is the frequency, v is the velocity of the object, and λ is the wavelength of the object's motion.

How do I determine the velocity of a moving object?

The velocity of a moving object can be determined by dividing the distance traveled by the time it takes to travel that distance. This can be represented by the equation v = d/t, where v is the velocity, d is the distance, and t is the time.

What is the relationship between wavelength and frequency of a moving object?

The relationship between wavelength and frequency of a moving object is inverse. This means that as the wavelength decreases, the frequency increases, and vice versa. This relationship is represented by the equation v = fλ, where v is the velocity, f is the frequency, and λ is the wavelength.

Can the frequency of a moving object change?

Yes, the frequency of a moving object can change. It can change if the velocity or wavelength changes. The frequency can also change if the object is affected by external forces such as gravity, friction, or air resistance.

Why is it important to calculate the frequency of a moving object?

Calculating the frequency of a moving object is important for understanding its behavior and characteristics. It can help determine the object's speed and direction of motion, as well as its interactions with other objects and forces. This information is crucial in various fields of science, including physics, engineering, and astronomy.

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