Calculating Frequency of Siren Heard by Truck After Police Passes

[sugz]

Homework Statement

A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren relative to the police car is 500 Hz, what is the frequency heard by an observer in the truck after the police car passes the truck? (The speed of sound in air is 343 m/s.)
a)396 Hz
b) 636 Hz
c)361 Hz
d)393 Hz
e)617 Hz

Homework Equations

f′ = [(v + vO)/(v − vS)]f

The Attempt at a Solution

Using the equation above, as they are moving away from each other, i made vO = -36 m/s and vS = -45m/s. Plugging in those values, I get 396 Hz, which is option a) however the correct answer appears to be 636 Hz, which can only be obtained assuming that they are moving towards each other.

 

[SteamKing]

Homework Statement

A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren relative to the police car is 500 Hz, what is the frequency heard by an observer in the truck after the police car passes the truck? (The speed of sound in air is 343 m/s.)
a)396 Hz
b) 636 Hz
c)361 Hz
d)393 Hz
e)617 Hz

Homework Equations

f′ = [(v + vO)/(v − vS)]f

The Attempt at a Solution

Using the equation above, as they are moving away from each other, i made vO = -36 m/s and vS = -45m/s. Plugging in those values, I get 396 Hz, which is option a) however the correct answer appears to be 636 Hz, which can only be obtained assuming that they are moving towards each other.

The way you have specified the velocities V_O and V_S, both the observer and the police car are moving in the same direction. Over time, the distance separating the truck from the police car should increase.

 

[sugz]

I'm sorry but I don't understand what you mean?

 

[thankz]

I get 636 but I added the cars velocities because they are moving AWAY from each other.

 

[sugz]

When they are moving away from each other, the equation becomes f' = [(v-vO)/(v+vs)]f. Thats what it says in our textbook, and when doing that, I get the value of 396Hz.

 

[thankz]

get rid of the negative signs when you do the equations.

 

[SteamKing]

I'm sorry but I don't understand what you mean?

If you make the velocity of the truck and the police car both negative, it implies that the two vehicles are traveling in the same direction, relative to a fixed point. Same deal if both velocities are positive. It stands to reason then, that if the truck and the police care are traveling in opposite directions, then their velocities must have different signs.