You are driving along a highway at 25 m/s when you hear the siren of an emergency vehicle traveling in the opposite direction on the other side of the highway. when the vehicle is approaching you, you hear the frequency of the siren as 2300 hz, but when it is past you the frequency becomes 1600 hz. what is the speed of the vehicle? the speed of sound in air is 343 m/s.

Explanation:

Let´s use Doppler effect, in order to calculate the speed of the vehicule. The Doppler effect equation for a general case is given by:

Where:

Now let's consider the next cases:

So, in this case:

Besides, the source and the observer both are in motion towards each other, hence:

Solving for

Finally, replacing the data provided:

The speed of the emergency vehicle is about 37 m/s

Let's recall the Doppler Effect formula as follows:

f' = observed frequency

f = actual frequency

v = speed of sound waves

v_o = velocity of the observer

v_s = velocity of the source

Let's tackle the problem!

Given:

initial observed frequency = f'_1 = 2300 Hz

final observed frequency = f'_2 = 1600 Hz

velocity of the observer = v_o = 25 m/s

speed of sound in air = v = 343 m/s

Asked:

speed of the source = v_s = ?

Solution:

We will use the formula of Doppler Effect.

When the vehicle is approaching you,

→ Equation 1

When the vehicle is past you,

→ Equation 2

Next, we will solve the two equations above by adding them ( Equation 1 + Equation 2 ):

Grade: College

Subject: Physics

Chapter: Sound Waves

Keywords: Sound, Wave , Wavelength , Doppler , Effect , Policeman , Stationary , Frequency , Speed , Beats