Final answer:
To calculate the phase difference in a progressive sine wave, you use the wave's wavelength and period along with the given distances or times. For two points 5.4 cm apart, the phase difference is 0.8308 * π radians, and for two instants separated by 0.021 s at a given point, it is 3π radians.
Step-by-step explanation:
The question involves calculating the phase difference in a progressive sine wave. The phase difference between two points in a wave can be calculated using the formula phase difference = (2π * distance) / wavelength. Similarly, the phase difference at a single point between two different times can be found using phase difference = (2π * time) / period.
Calculations:
(a) Phase Difference Between Two Points
The wavelength, λ, is given as 13 cm. The distance between the points is 5.4 cm. Therefore, the phase difference is: (2π * 5.4 cm) / 13 cm = (2π * 0.4154) = 0.8308 * π radians.
(b) Phase Difference Between Two Instants
The period, T, is 0.014 s. The time difference between the two instants is 0.021 s. Thus, the phase difference is: (2π * 0.021 s) / 0.014 s = (2π * 1.5) = 3π radians.
completed question:
A progressive sine wave has a wavelength of 13 cm and a period of 0.014 s. Determine the phase difference (a) between two points 5.4 cm apart; (b) at a given point but between two instants separated by 0.021 s.