Question

A driver travels northbound on a highway at a speed of 20.0 m/s. A police car, traveling southbound at a speed of 43.0 m/s, approaches with its siren producing sound at a frequency of 2600 Hz. (a) What frequency does the driver observe as the police car approaches?
...................... Hz
(b) What frequency does the driver detect after the police car passes him?
..........................Hz
(c) Repeat parts (a) and (b) for the case when the police car is traveling northbound. while police car overtakes ....................Hz
after police car passes .....................Hz

Answer 1

Answer:

Explanation:

Let the velocity of observer the driver be V₀ and the velocity of police car the source be$v_s$. Let V be the velocity of sound in air.

The apparent  frequency f is given by the following relation

$\frac{f}{F} = \frac{V+V_0}{V-V_s}$

F is real frequency.

Now F = 2600,

$V_0 = 20 ms^{-1} and\\\ V_s= 40ms^{-1}$

Putting these values in the equation

$\frac{f}{2600} = \frac{343+20}{343-43}$

f = 3146 Hz.

b ) After the police passes , the sign of velocity of observer and source get reversed.

$\frac{f}{2600} = \frac{343-20}{343+43}$

f = 2175 Hz

c ) When the police car is also going northward and trying to overtaking the driver the frequency is calculated as follows .

$\frac{f}{2600} = \frac{343-20}{343-43}$

f = 2799 Hz

When the policy car already crosses the drives the frequency will be as follows

$\frac{f}{2600} = \frac{343+20}{343+43}$

f = 2445 Hz

Answer 2

The frequency of the siren for driver car, changes with change in the direction and the speed of the police car.

• (a) Frequency does the driver observe as the police car approaches is 3146 Hz.
• (b) Frequency does the driver detect after the police car passes him is 2175 Hz.

• (c) When the police car is traveling northbound,.

• i) Frequency while police car overtakes is 2799 Hz.

• ii) Frequency after police car passes is 2455 Hz.

What is the intensity of the sound?

Intensity of the sound is the intensity flowing per unit area which is perpendicular to the direction of sound wave travelling in.

The intensity of the sound wave is inversely proportional to the distance of the object and source of sound wave.

The speed of the driver travels northbound on a highway is 20.0 m/s and the speed of the police car travels southbound on a highway is 43.0 m/s.

• (a) Frequency does the driver observe as the police car approaches-

The frequency of the siren of police car is 2600 Hz. As the police car approaches then the siren frequency can be find out using the following formula.

As the speed of the sound is 343 m/s. Thus using the formula of apparent frequency, we get,

$f=2600\times\dfrac{343+20}{343-43}\\f=3146\rm Hz$

• (b) Frequency does the driver detect after the police car passes him-

Now the police car passes. Thus the speed of light should be added to the speed of police car and subtracted to the speed of driver in the above formula as,

$f=2600\times\dfrac{343-20}{343+43}\\f=2175\rm Hz$

• (c) When the police car is traveling northbound,

Frequency while police car overtakes-

As both the car travelling northbound. Thus the speed should be subtracted in overtake conditions as,

$f=2600\times\dfrac{343-20}{343-43}\\f=2799\rm Hz$

Frequency after police car passes-

As both the car travelling southbound. Thus the speed should be added in passing conditions as,

$f=2600\times\dfrac{343+20}{343+43}\\f=2455\rm Hz$

The frequency of the siren for driver car, changes with change in the direction and the speed of the police car.

• (a) Frequency does the driver observe as the police car approaches is 3146 Hz.
• (b) Frequency does the driver detect after the police car passes him is 2175 Hz.

• (c) When the police car is traveling northbound,.

• i) Frequency while police car overtakes is 2799 Hz.

• ii) Frequency after police car passes is 2455 Hz.

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