A progressive wave equation is represented by y = a sin(150 \pit - \(\frac{\pix}{4}\)). if the phase difference of a progressive wave is 45^\circ, the value of x in the equation is
A
3 cm
B
4 cm
C
1 cm
D
2 cm
Verified Correct Answer: C.
Physical Principles & Numerical Solution
Y = sin \pi(150\pit - \(\frac{\pix}{4}\))
Comparing the above with the standard wave equation:
Y = A sin \pi (\(\frac{(2vt)}{\lambda}\) - \(\frac{(2x)}{\lambda}\))
=> the phase difference \(\frac{x}{4}\) = \(\frac{2x}{\lambda}\)
∴ \(\frac{1}{4}\) = \(\frac{2}{\lambda}\) => \lambda = 8cm
∴ \(\frac{2\pix}{8}\) = 45^\circ
since \pi = 180^\circ
45^\circ X 8 = 2 X 180^\circ x
∴ x = 1cm
Source: Myschool Past Questions Archive (Record #14334)