A progressive wave is represented by \( y = 10 \text{Sin} (1000\pi t - \frac{\pi x}{34}) \) . two layers of the wave separated by 153cm have a phase difference of?
A
2700
B
450
C
900
D
1800
E
No Correct Option
Verified Correct Answer: C.
Physical Principles & Numerical Solution
Comparing \( y = 10 \text{Sin} (1000\pi t - \frac{\pi x}{34}) \) with y = A sin (\omegat - ϕ)
where ϕ = \(\frac{2\pi x}{\lambda}\)
comparing: \(\frac{2\pi x}{\lambda}\) = \( \frac{\pi x}{34}\)
\lambda = 34 \(\times\) 2 = 68
: ϕ = \(\frac{2\pi x}{\lambda}\) = \(\frac{2\pi \times 153}{68}\)
ϕ = 4.5\(\pi\) rad = 810^\circ or 90^\circ
since sin 810^\circ or 90^\circ = 1
Source: Myschool Past Questions Archive (Record #41400)