How Does the Doppler Effect Influence the Frequency of an Ambulance Siren?

[Lizziecupcake]

So I'm having a hard time getting the second part of the problem, so could anyone help me

An ambulance travels down a highway at a speed of 65.0 mi/h, its siren emitting sound at a frequency of 4.10 102 Hz. Take the speed of sound in air to be v = 345 m/s. What frequency is heard by a passenger in a car traveling at 56.0 mi/h in the opposite direction as the car and ambulance

a)approach each other: 480.2 Hz
b)pass and move away from each other?: 370.7 Hz

Repeat this problem, but assume the ambulance and the car are going in the same direction, with the ambulance initially behind the car. The speeds and frequency of the siren are the same as in the example.
(a) Find the frequency heard before the ambulance passes the car.
(b) Find the frequency heard after the ambulance passes the car. [Note: The highway patrol subsequently gives the driver of the car a ticket for not pulling over for an emergency vehicle!]

So far I tried to do the same as the first part by changing the speed because I'm not exactly sure what to do.

The equation used is:
fO= fS(v + vO)/(v - vS)

 

[PeterO]

So I'm having a hard time getting the second part of the problem, so could anyone help me

An ambulance travels down a highway at a speed of 65.0 mi/h, its siren emitting sound at a frequency of 4.10 102 Hz. Take the speed of sound in air to be v = 345 m/s. What frequency is heard by a passenger in a car traveling at 56.0 mi/h in the opposite direction as the car and ambulance

a)approach each other: 480.2 Hz
b)pass and move away from each other?: 370.7 Hz

Repeat this problem, but assume the ambulance and the car are going in the same direction, with the ambulance initially behind the car. The speeds and frequency of the siren are the same as in the example.
(a) Find the frequency heard before the ambulance passes the car.
(b) Find the frequency heard after the ambulance passes the car. [Note: The highway patrol subsequently gives the driver of the car a ticket for not pulling over for an emergency vehicle!]

So far I tried to do the same as the first part by changing the speed because I'm not exactly sure what to do.

The equation used is:
fO= fS(v + vO)/(v - vS)

No doubt you did the first part using a closing speed of 121 mi/h and a separating speed of 121 mi/h [ie 65 + 56]

With the vehicles travelleing in the same direction, the closing and opening speeds are just 9 mi/h [ie 65 - 56]

 

[Lizziecupcake]

Can you clarify a bit more, I'm still confused. Also, I converted the speeds into m/s

 

[PeterO]

Can you clarify a bit more, I'm still confused. Also, I converted the speeds into m/s

Please show the full calculations for your 480.2 answer.

 

[asteriatic]

The Doppler Effect is a phenomenon that occurs when there is relative motion between a source of sound and an observer. In this case, the ambulance is the source of sound and the passenger in the car is the observer. As the ambulance and the car move towards each other, the frequency of the sound waves emitted by the siren will appear to increase to the observer due to the compression of the waves. This is known as the "approach effect" and can be calculated using the equation fO= fS(v + vO)/(v - vS), where fO is the observed frequency, fS is the source frequency, v is the speed of sound, vO is the observer's speed, and vS is the source's speed.

In the first part of the problem, the ambulance and the car are moving towards each other, so the observed frequency will be higher than the source frequency. Using the given values, we can calculate the observed frequency to be 480.2 Hz.

In the second part of the problem, the ambulance and the car are moving in the same direction, with the ambulance initially behind the car. As the ambulance passes the car, the frequency of the sound waves will appear to decrease to the observer due to the stretching of the waves. This is known as the "recede effect" and can also be calculated using the same equation.

Before the ambulance passes the car, the observer will hear a frequency of 370.7 Hz. After the ambulance passes the car, the observer will hear a frequency of 480.2 Hz.

It is important to note that the observed frequencies in both cases are different from the source frequency of 4.10 102 Hz. This is because of the relative motion between the source and the observer.

In conclusion, the Doppler Effect is an important concept in understanding how sound waves behave in different situations. In the case of an emergency vehicle, it is crucial for drivers to be aware of the change in frequency of the siren as it approaches or passes by, in order to safely make way for the vehicle.