Why Does T0 Appear in the Doppler Effect Equation?

[logearav]

Homework Statement

Revered members,
I have attached the image of Doppler effect explanation.

Homework Equations

I have the following doubts
1)t₁ = L/v
2) t₂ = T₀ +( L + v_sT₀)/v
But why T₀ comes here, instead of ( L + v_sT₀)/v

The Attempt at a Solution

 

[Spinnor]

A stationary source emits waves of frequency F and period 1/F. The period is the time it takes successive wave fronts to reach you. How does the period change when the source moves away from you? First you need to know how far the source moves in the time 1/F, that is simply 1/F times the source velocity v_s. Now how much is the period lengthened? By the extra time it takes wave to go the extra distance v_s/F which is delta_t =v_s/Fv where v is the wave velocity. So the new period between wave fronts of a moving source is

1/F' = 1/F + v_s/Fv = 1/F(1+ v_s/v)

Makes more sense to me thinking of the period then the frequency?

If you are troubled by what is written derive the formula yourself.

 

[logearav]

A stationary source emits waves of frequency F and period 1/F. The period is the time it takes successive wave fronts to reach you. How does the period change when the source moves away from you? First you need to know how far the source moves in the time 1/F, that is simply 1/F times the source velocity v_s.

Now how much is the period lengthened? By the extra time it takes wave to go the extra distance v_s/F which is delta_t =v_s/Fv where v is the wave velocity.

Thanks for the reply Spinnor. I don't understand the line given in quote.

 

[Spinnor]

Lets say you are in a car and beep your horn once a second. Everyone who is at rest relative to the car will also hear the horn beep once a second. Now suppose you drive away from me at some large velocity, say 1/6 the speed of sound all the while beeping your horn once a second. With this information you should be able to compute the amount of time I hear between beeps. Yes? It will be longer then one second because the beep has longer to travel. You only need three numbers, the period of the beeps, the velocity of the car, and the velocity of sound in air.

 

[rwisz]

The Doppler effect is a well-studied phenomenon in the field of physics and has been extensively researched and observed in various experiments. It is a change in the frequency or wavelength of a wave due to the relative motion of the source and observer. This effect is commonly observed in everyday life, such as the change in pitch of a siren as an ambulance passes by.

In regards to your doubts, it is important to understand that the equations you have provided are specific to a certain scenario and may not apply universally to all situations involving the Doppler effect. The equation t1 = L/v is used to calculate the time it takes for a wave to travel a distance L at a constant velocity v. This equation does not involve T0, as it is not relevant in this scenario.

The second equation t2 = T0 + (L + vsT0)/v is used to calculate the time it takes for the wave to reach the observer when the source is moving at a constant velocity vs. In this scenario, T0 represents the initial time, or the time it takes for the wave to reach the observer when the source is at rest. This equation includes T0 because the source is now in motion, and the observer must factor in the additional time it takes for the wave to travel the distance L due to the source's motion.

It is important to remember that equations and formulas in science are derived from observations and experiments and may not always make intuitive sense. However, they have been proven to accurately describe the behavior of physical phenomena, including the Doppler effect. I would suggest further research and study on the topic to gain a deeper understanding of these equations and their applications.