the angular frequency of a particle in a progressive wave in an elastic medium is 100.(3.14) rads^-1.and it is moving with a velocity of 200 ms^-1. the phase difference between two particles separated by a distance of 20cm is
options:
1.31.4 rad
2.36 rad
λ=2•π•v/ω,
Δφ = 2•π•Δx/λ =
= ω•Δx/v
To find the phase difference between two particles separated by a distance in a progressive wave, you need to use the formula:
Phase Difference = (2π / λ) * x
Where:
- Phase Difference is the angle (in radians) by which one particle is ahead or behind the other.
- λ (lambda) is the wavelength of the wave.
- x is the distance between the two particles.
First, let's calculate the wavelength (λ). The formula to find the wavelength is:
λ = v / f
Where:
- λ (lambda) is the wavelength of the wave.
- v is the velocity of the particle.
- f is the frequency of the wave.
Given that the angular frequency (ω) of the wave is 100(3.14) rad/s, we can find the frequency (f) using the formula:
ω = 2πf
Rearranging the formula, we get:
f = ω / (2π)
Substituting the angular frequency into the equation:
f = 100(3.14) / (2π)
f ≈ 50 Hz
Now, substitute the velocity (v = 200 m/s) and the calculated frequency (f = 50 Hz) into the wavelength formula:
λ = v / f
λ = 200 / 50
λ = 4 m
Finally, substitute the wavelength (λ = 4 m) and the distance (x = 20 cm = 0.2 m) into the phase difference formula:
Phase Difference = (2π / λ) * x
Phase Difference = (2π / 4) * 0.2
Phase Difference = π * 0.1
Phase Difference ≈ 0.314 rad
Therefore, the phase difference between the two particles separated by a distance of 20 cm is approximately 0.314 radians.