How does the phase of a wave change over time at a given position?

[yuihatano]

Homework Statement

A 403 Hz wave travels at 200 m/s along a wire.

a)At a given time, the distance between points that differ in phase by 1.9 rad is ___ m.
b)At a given position, the change in phase during an interval of 4.8 ms is ___ rad.

Homework Equations

V=w/k
w=2pif

The Attempt at a Solution

I 've already solved for a), it was pretty straight forward. Now, I'm stuck on b)

w=2pif
=2pi*403
=806pi

v=w/k
k=w/v
=806pi/200
=4.03pi

delta phi = x/k
= 1.9/4.03pi
=0.15m
this was for number 1... now I'm stuck on b)
pls help...

 

[ehild]

The wave is periodic both in time and position. The displacement in a sine wave is

u=A*sin(2p(t/T-x/lambda)) or in other form u=A*sin(wt-kx),

with w=2pi/T and k=2pi/lambda.

The term 2pi(t/T-x/lambda)=wt-kx is the phase of the wave.

T is the time period and the period in space is lambda. At a given time t, two points which are lambda distance apart differ by 2pi in phase. At a certain position x, the phase changes by pi during T time interval.

You know the frequency f, so you know the time period T=1/f. The elapsed time is given, dt=4.8*10^-3 s, what is the phase difference between t and t+dt?

ehild

 

[yuihatano]

The wave is periodic both in time and position. The displacement in a sine wave is

u=A*sin(2p(t/T-x/lambda)) or in other form u=A*sin(wt-kx),

with w=2pi/T and k=2pi/lambda.

The term 2pi(t/T-x/lambda)=wt-kx is the phase of the wave.

T is the time period and the period in space is lambda. At a given time t, two points which are lambda distance apart differ by 2pi in phase. At a certain position x, the phase changes by pi during T time interval.

You know the frequency f, so you know the time period T=1/f. The elapsed time is given, dt=4.8*10^-3 s, what is the phase difference between t and t+dt?

ehild

Thank you!