# Question on a doppler effect problem and equation

• Kalix
In summary, the problem involves two trains moving towards each other, with speeds of 130 km/hr and 90 km/hr respectively. Train #2 emits a frequency of 500 Hz. To find the frequency heard by the engineer on train #1, the equation f_o = f_s (v + v_o)/(v - v_s) can be applied, where v is the speed of sound and v_o and v_s are the speeds of the observer and source respectively. In this case, the numerator would be positive and the denominator negative.
Kalix

## Homework Statement

Question: Two trains on separate tracks move toward one another. Train #1 has a speed of 130 km/hr and train #2 a speed of 90km/hr. Train 2 blows its horn, emitting a frequency of 500 Hz. What frequency is heard by the engineer on train #1?

## Homework Equations

This is where I get stuck. Because this is a problem where two objects are moving towards each other their is no set equation according to my teacher. You have to "make one up" depending on the problem. So here are the equations I know.

Source is moving and the observer is stationary:
fo=fs(v/v-vs) For a source moving toward stationary observer. frequency goes up
fo=fs(v/v+vs) For a source moving away from a stationary observer. frequency goes down

Source is stationary and the observer is moving:
fo=fs(1-vo/v) For a source moving away from a stationary source. frequency goes down
fo=fs(1+vo/v) For a source moving toward a stationary source. frequency goes up

I don't understand how to get equations for a problem where both objects are moving from these equations above.

## The Attempt at a Solution

First I converted 130km/hr to m/s and got 36.1m/s. I did the same with the 90km/hr and got 25m/s.
Vo=36.1m/s
Vs=25m/s
Fs=500Hz
v=331
Fo(train #1)=?

I know all the terms I just don't know what equation to use.

In these situations, this equation can be applied (proof might be a bit tricky though):

$f_{o}= f_{s} \large \frac{v \pm v_{o}}{v \pm v_{s}}$

Where you would choose the signs of the basis of the convention you mentioned. For example, in your case, the numerator would be plus, and the denominator minus.

## 1. How do you calculate the doppler effect?

The doppler effect can be calculated using the following equation: f' = f(v + vd)/(v + vs), where f' is the observed frequency, f is the source frequency, v is the speed of sound, vd is the velocity of the detector, and vs is the velocity of the source.

## 2. What is the doppler effect used for?

The doppler effect is used to explain the change in frequency of a wave as it is perceived by a detector that is either moving towards or away from the source of the wave.

## 3. How does the doppler effect affect sound waves?

The doppler effect can cause an increase or decrease in the perceived frequency of a sound wave, depending on the relative velocities of the source and detector.

## 4. What is the difference between the doppler effect for sound waves and light waves?

The main difference is that the doppler effect for light waves is affected by the relative velocities of the source and detector as well as the speed of light, while the doppler effect for sound waves is only affected by the relative velocities and the speed of sound.

## 5. Can the doppler effect be observed in everyday life?

Yes, the doppler effect can be observed in many everyday situations, such as the change in pitch of a siren as an ambulance or police car passes by, or the change in pitch of a train horn as it approaches and then passes by a stationary observer.

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