Answer:
a) Two points that differ in phase by π/8 rad are 0.0461 m apart.
b) The phase difference between two displacements at a certain point at times 1.6 ms apart is 4π/3.
Explanation:
f = 420 Hz, v = 310 m/s, λ = wavelength = ?
v = fλ
λ = v/f = 310/420 = 0.738 m
T = periodic time of the wave = 1/420 = 0.00238 s = 0.0024 s = 2.4 ms
a) Two points that differ in phase by π/8 rad
In terms of the wavelength of the wave, this is equivalent to [(π/8)/2π] fraction of a wavelength,
[(π/8)/2π] = 1/16 of a wavelength = (1/16) × 0.738 = 0.0461 m
b) two displacements at times 1.6 ms apart.
In terms of periodic time, 1.6ms is (1.6/2.4) fraction of the periodic time.
1.6/2.4 = 2/3.
This means those two points are 2/3 fraction of a periodic time away from each other.
1 complete wave = 2π rad
Points 2/3 fraction of a wave from each other will have a phase difference of 2/3 × 2π = 4π/3.
