Question

The amplitudes and phase differences for four pairs of waves of equal wavelengths are (a) 2 mm, 6 mm, and π rad; (b) 3 mm, 5 mm, and π rad; (c) 7 mm, 9 mm, and π rad; (d) 2 mm, 2 mm, and 0 rad. Each pair travels in the same direction along the same string. Without written calculation, rank the four pairs according to the amplitude of their resultant wave, greatest first. (Hint: Construct phasor diagrams.)

Answer 1

a = d > b = c

Step-by-step explanation:

The information about amplitudes and phase differences for four pairs of waves of equal wavelengths are given below:

(a) 2 mm, 6 mm, and π rad

(b) 3 mm, 5 mm, and π rad

(c) 7 mm, 9 mm, and π rad

(d) 2 mm, 2 mm, and 0 rad

Whenever a wave has zero phase difference, its amplitude of the resultant wave will be twice the amplitude of any of the two waves. Nevertheless, let assume that the amplitude is a vector having angle Ø between them. The resultant vector will help us rank the four pairs according to the amplitude of their resultant wave by using phasor diagrams.

a.) 6 - 2 = 4mm

b.) 5 - 3 = 2mm

c.) 9 - 7 = 2mm

d.) 2 + 2 = 4mm

Therefore,

a = d and b = c

a = d > b = c

Please find the attached file for the phasor diagrams