Calculating Wave Packet Length & Frequency for Radar Transmitter

EngageEngage
Messages
203
Reaction score
0

Homework Statement


A radar transmitter used to measure the speed of pitched baseballs emits pulses of 2.0cm wavelength that are .25micros 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

The Attempt at a Solution


I think I have (a) right: Length of the wave packet is the time of the pulse times the speed of the wave.
L=c*t = 75m.

(b) This is what I'm not sure on. Must the receiver be tuned for the group frequency or the phase frequency? If I'm thinking about this right, these pulses should make beats.

The group frequency will be: 1/(.25micros), right? This is the frequency of the modulation wave.

The phase frequency would be c/.02m, right? This is the frequency of the wave 'inside' the modulation wave.

Or am I completely misunderstanding the problem?

(c) The bandwidth, if I am not mistaken is dw, (spread of angular frequency).
dw*dt~1
Would dt here just be the .25micros?

If anyone could tell me if I am doing this right and help me out, I would appreciate it.
 
Physics news on Phys.org
(b) The receiver is tuned for phase frequency.

(c) Correct -- might be an extra factor of pi or 2*pi, I'm not sure about the exact relation.
 
thank you for the help
 

Thread 'Direction of the magnetic field of an oscillating charge'

Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
View full post »

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
View full post »

Similar threads

Wave dispersion and the bandwidth theorem
Replies
2
Views
5K
Optical-EME for licensed amateur radio operators
Replies
19
Views
1K
Frequency Bandwidth of Detecting and Amplifying
Replies
1
Views
2K
How Long Is the Wave Packet from a Radar Transmitter?
Replies
4
Views
5K
B Waves in space
Replies
10
Views
3K
How Does Pulse Duration Affect Frequency Spread in a Gaussian-Enveloped Laser?
Replies
1
Views
2K
How to interpret this Wave Equation (Derivation) Help ?
Replies
4
Views
2K
Am vs Fm variable capacitor receiver, what is the difference?
Replies
2
Views
2K
Description of a wave packet incident on a square potential barrier
Replies
1
Views
2K
Minimum Frequency of FM Data / Catastrophic Error Scenario?
2
Replies
68
Views
5K

Hot Threads

Recent Insights

Back
Top