Aradar station sends out a 25 hz sound wave at a speed of 340 m/s. the sound wave bounces off a weather ballon and returns back to the radar station in 4.8s at a frequency of 24 hz. how far away from the radar station is the ballon and what direction is it moving?

Answers:

a)The balloon is 68 m away of the radar station

b) The direction of the balloon is towards the radar station

Explanation:

We can solve this problem with the Doppler shift equation:

 (1)

Where:

is the actual frequency of the sound wave

is the "observed" frequency

is the velocity of sound

is the velocity of the observer, which is stationary

is the velocity of the source, which is the balloon

Isolating :

 (2)

 (3)

(4) This is the velocity of the balloon, note the negative sign indicates the direction of motion of the balloon: It is moving towards the radar station.

Now that we have the velocity of the balloon (hence its speed, the positive value) and the time () given as data, we can find the distance:

(5)

(6)

Finally:

(8) This is the distance of the balloon from the radar station

what is the actual question though?