Question

A radar station sends out a 250000 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 240000 hz. How far away from the radar station is the ballon and what direction is it moving?

Answer 1

Answers:

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

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

Step-by-step explanation:

We can solve this problem with the Doppler shift equation:

`f'=(V+V_(o))/(V-V_(s)) f` (1)

Where:

`f=250,000 Hz` is the actual frequency of the sound wave

`f'=240,000 Hz` is the "observed" frequency

`V=340 m/s` is the velocity of sound

`V_(o)=0 m/s` is the velocity of the observer, which is stationary

`V_(s)` is the velocity of the source, which is the balloon

Isolating
`V_(s)`:

`V_(s)=(V(f'-f))/(f')` (2)

`V_(s)=(340 m/s(240,000 Hz-250,000 Hz))/(240,000 Hz)` (3)

`V_(s)=-14.16 m/s` (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 (
`t=4.8 s`) given as data, we can find the distance:

`d=V_(s)t` (5)

`d=(14.16 m/s)(4.8 s)` (6)

Finally:

`d=68 m` (8) This is the distance of the balloon from the radar station