"What is the phase difference of a progressive wave [y=0.5sin(2πx-60t] with a phase shift from (-2,0)to(1.5,0)"?
I dont speak smarty pants
How long is the wave ?
Well say for example at t = 0
then at x = 0 you have y = 0.5 sin 0 = 0
at x = 1/2 you have y = 0.5 sin pi
at x = 1you have y = 0.5 sin 2 pi = 0
so when x changed 1, our wave we went a full cycle
wavelength = 2 pi
now
what fraction of a wavelength are we talking about
- 2 to + 1.5 = 3.5
3.5 / 1 = 3.5
so we went 3 1/2 wavelengths
that is three cycles + half a cycle
that is 6 pi + pi = 7 pi in radians
To find the phase difference of a progressive wave, you need to compare the phase at two different points on the wave. In this case, we are given the equation of the wave: y = 0.5sin(2πx - 60t).
To calculate the phase difference between two points, we need to determine the phase at each point and then find the difference between them.
The general equation for the phase of a sine wave is φ = kx - ωt, where k is the wave number and ω is the angular frequency.
Let's break down the given equation to find the values of k and ω:
y = 0.5sin(2πx - 60t)
Comparing it with the general phase equation, we can identify that k = 2π and ω = 60.
Now, let's calculate the phase at each of the given points: (-2, 0) and (1.5, 0).
For the point (-2, 0):
φ1 = kx1 - ωt1
= 2π(-2) - 60(0)
= -4π
For the point (1.5, 0):
φ2 = kx2 - ωt2
= 2π(1.5) - 60(0)
= 3π
Finally, to find the phase difference, we subtract φ1 from φ2:
Phase Difference = φ2 - φ1
= (3π) - (-4π)
= 7π
Therefore, the phase difference of the progressive wave is 7π.