# Homework Help: Simple wave packets problem

1. Mar 17, 2012

### lockedup

1. The problem statement, all variables and given/known dataA radar transmitter used to measure the speed of pitched baseballs emits pulses of 2.0 cm wavelength that are .25 μs in duration. a) What is the length of the wave packet produced? b) To what frequency should the receiver be tuned? c) What must be the minimum bandwidth of the receiver?

2. Relevant equations
ΔkΔx≈1
ΔωΔt≈1

3. The attempt at a solution
Part c) was easy enough. ΔωΔt≈1 → Δω≈1/Δt = 1/.00000025 = 4000000

4000000/2π = 6.36e5 Hz

The others? I have no idea. The section of the text barely defines what a wave packet is and I've read through it at least three times.

I would appreciate some help getting started.

2. Mar 17, 2012

### marcusl

a) What is the propagation speed of radio waves? What physical length does a 0.25 us pulse correspond to?
b) You know the wavelength, what frequency does that correspond to?

3. Mar 17, 2012

### lockedup

a) v = .02 m/.00000025 s = 80000 m/s What do I do now?

b) Ooh... *facepalm* f = c/λ = 3e8/.02 = 1.5e10

4. Mar 17, 2012

### marcusl

b is correct, a not at all. What is the speed of light?

5. Mar 17, 2012

### lockedup

3e8(.25e-6) = 75

*facepalm again* Thank you