contestada

Part 1) A cop car traveling at 25 m/s has a siren producing a frequency of 700 Hz. A felon jumps on his motorcycle and speed off in the opposite direction of 15 m/s. What frequency does the felon hear as he sped away (speed of sound is 343 m/s)?
Part 2) The cop does a U-turn and speeds towards the felon at 30 m/s, while the felon speeds up to 20 m/s. What frequency does the felon hear as he sped away (speed of sound is 343 m/s)?
Part 3) What if the felon then sped up to 30 m/s and all other conditions remained the same?

Respuesta :

skyluke89

1) 621.8 Hz

2) 719.3 Hz

3) 700 Hz

Explanation:

1)

The Doppler effect occurs when there is a source of a wave in relative motion with respect to an observer.

When this happens, the frequency of the wave appears shifted to the observer, according to the equation:

[tex]f'=\frac{v\pm v_o}{v \pm v_s}f[/tex]

where

f is the real frequency of the sound

f' is the apparent frequency of the sound

v is the speed of the sound wave

[tex]v_o[/tex] is the velocity of the observer, which is negative if the observer is moving away from the source, positive if the observer is moving towards the source

[tex]v_s[/tex] is the velocity of the source, which is negative if the source is moving towards the observer, positive if the source is moving away

In this problem we have:

f = 700 Hz is the frequency of the siren

v = 343 m/s is the speed of sound

[tex]v_s=-25 m/s[/tex] is the velocity of the car with the siren

[tex]v_o = +15 m/s[/tex] is the velocity of the felon (he's moving away from the siren)

So, the frequency heard by the felon is

[tex]f=\frac{343-25}{343+15}(700)=621.8 Hz[/tex]

2)

In this case, the cop does a U-turn and speeds towards the felon at 30 m/s.

This means that now the siren is moving towards the observer (so, [tex]v_s[/tex] becomes positive), while the sign of [tex]v_o[/tex] still remains positive.

So we have:

f = 700 Hz is the frequency of the siren

v = 343 m/s is the speed of sound

[tex]v_s=+30 m/s[/tex] is the velocity of the car with the siren

[tex]v_o = +20 m/s[/tex] is the velocity of the felon

So, the frequency heard by the felon is

[tex]f=\frac{343+30}{343+20}(700)=719.3 Hz[/tex]

3)

In this case, the felon speeds up to 30 m/s.

This means that now the felon and the siren are moving with the same relative velocity: so, it's like they are not moving relative to each other, so the frequency will not change.

In fact we have:

f = 700 Hz is the frequency of the siren

v = 343 m/s is the speed of sound

[tex]v_s=+30 m/s[/tex] is the velocity of the car with the siren

[tex]v_o = +30 m/s[/tex] is the velocity of the felon

So, the frequency heard by the felon is

[tex]f=\frac{343+30}{343+30}(700)=700 Hz[/tex]

So, the frequency will not change.

Otras preguntas