Wave Packets Uncertainty Principle - Wave Packets

[curto]

Uncertainty Principle - Wave Packets

Homework Statement

If a phone line is capable of transmitting a range of frequencies delta(f) = 5,431 Hz, what is the approximate duration of the shortest pulse that can be transmitted over the line? Give your answer in millseconds to 4 significant figures and take delta(E)*delta(t) ~ h.

Homework Equations

we have:

[tex]\Delta[/tex]E[tex]\Delta[/tex]t = h
[tex]\Delta[/tex]E = v[tex]\Delta[/tex]p
p = h/[tex]\lambda[/tex]

so using ^^^ we have:

[tex]\Delta[/tex]p = h[tex]\Delta[/tex][tex]\nu[/tex]/c

correct?

The Attempt at a Solution

using:

[tex]\Delta[/tex]p = h[tex]\Delta[/tex][tex]\nu[/tex]/c

i find the uncertainty in p to be ~1.2E-38
then using:

[tex]\Delta[/tex]E = v[tex]\Delta[/tex]p where v = c (electron flow travels at the speed of light, correct?)

then using my value of the uncertainty of E to be ~3.6E-30 i used:

[tex]\Delta[/tex]E[tex]\Delta[/tex]t = h

to find my uncertainty in t to be ~0.1841 ms (4 sig. figures)

can anyone find any problems in my working? i don't know the actual answer but if my working is correct then its got to be right, yeah?

another way to do this (easier way that i only just found out about) is by using [tex]\Delta[/tex][tex]\nu[/tex][tex]\Delta[/tex]t ~ 1

since we are given [tex]\Delta[/tex][tex]\nu[/tex] in the question i just plugged that number in and got out 0.1841 ms (4 sig. figures) in one go

 

[lippyka]

!idk if this is the correct way to do it but it seems to work and its simpler than what i did above. any thoughts?