The discussion revolves around finding the distance between two points on a wave described by the equation y = 0.001 cos (7.5x + 15t) that have a phase difference of 45 degrees at the same instant in time. The subject area includes wave mechanics and phase relationships.
There is an ongoing exploration of the problem with participants sharing their reasoning and calculations. Some participants express confidence in their approach, while others seek clarification on units and graphing methods. Guidance has been offered regarding the exclusion of time dependency for graphing purposes.
Participants mention the assumption of SI units and the lack of explicit unit specifications in the problem statement. There is also a consideration of whether to use mks or cgs units.
Lavabug said:Homework Statement
For the given wave on a string:
y = 0.001 cos (7.5x + 15t)
find the distance between two points which have a phase difference of 45 degrees at the same instant in time.
The Attempt at a Solution
No idea how to solve this. Please help.
Lavabug said:I think I'm on to something:
The phase between the start and the end of a full wavelength is 2pi (full cycle).
For half a wavelength that's pi
For a quarter wavelength that's pi/2 or 90 degrees, ie: the phase between maxes and mins.
For an 1/8 of a wavelength the phase is pi/4, or 45 degrees.
The problem gives me the wavenumber so I can find the wavelength: 2pi/7.5 = lambda
So I think I can draw the following similarity:
lambda is to 2pi as
lambda/8 is to pi/4 ?
So the distance between points that represent a phase of 45 degrees is 1/8 of a wavelength?
Lavabug said:I'm pretty sure the units are just SI. I got my wavelength from the given wavenumber(7.5): lambda = 2pi/7.5 (don't have a calculator on hand lol).
The distance between points with 45 degree would be an eighth of that quantity.
So my idea is correct?
Lavabug said:How would I graph it? Can I exclude the time dependency (angfreq*t) and just plot .001cos(kx)?