Plane waves, phase difference question

[goldilocks]

Homework Statement

Consider a lightwave having a phase velocity of 3 x 10^8 m/s and a frequency of 6 x 10^14 hz. What is the shortest distance along the wave between any two points that have a phase difference of 30 degrees ? What phase shift occurs at a given point in 1 microsecond and how many waves have passed by in that time ?

Homework Equations

velocity = frequency x wavelength

The Attempt at a Solution

have calculated that the wavelength is 5000m, by dividing speed of light by the frequency, but am stuck and don't know how to proceec. any help would be amazing, thank you!

 

[rl.bhat]

When the distance between the two points is equal to the wavelength, the phase difference between the points is 2π. So when the phase difference between the two points is π/6, the distance between the two points is...

 

[tomcue]

I can provide a response to this question. First, you are correct in calculating the wavelength to be 5000m. This means that every 5000m along the wave, the phase will repeat itself.

To find the shortest distance between two points with a phase difference of 30 degrees, we can use the equation d = λ * θ/360, where d is the distance, λ is the wavelength, and θ is the phase difference. Plugging in the values, we get d = 5000m * 30/360 = 416.67m. This means that if you were to measure the phase at two points 416.67m apart, you would see a phase difference of 30 degrees.

Next, to find the phase shift at a given point in 1 microsecond, we can use the equation φ = ω * t, where φ is the phase shift, ω is the angular frequency (2πf), and t is the time. Plugging in the values, we get φ = (2π * 6 x 10^14 Hz) * (1 x 10^-6 s) = 1.2 x 10^9 radians. This means that the phase at that point will have shifted by 1.2 x 10^9 radians in 1 microsecond.

Finally, to find the number of waves that have passed by in 1 microsecond, we can use the equation N = f * t, where N is the number of waves, f is the frequency, and t is the time. Plugging in the values, we get N = (6 x 10^14 Hz) * (1 x 10^-6 s) = 6 x 10^8 waves. This means that in 1 microsecond, 6 x 10^8 waves will have passed by at that given point.

I hope this helps clarify the concepts and equations involved in solving this problem. Let me know if you have any further questions.