Question

The wave functions of two waves traveling in the same direction are given below. The two waves have the same frequency, wavelength, and amplitude, but they differ in their phase constant.

y1 (x,t) = 2 sin⁡(2πx ‒ 20πt), and

y2 (x,t) = 2 sin(2πx ‒ 20πt + φ),

a)where, y is in centimetres, x is in meters, and t is in seconds.

Which of the following wave functions represents the resultant wave due to the interference between the two waves:

1)y_result (x,t) = 4 sin⁡(2πx ‒ 20πt + φ)

2)y_result (x,t) = 2 sin⁡(πx ‒ 10πt + φ/2)

3)y_result (x,t) = 4 cos⁡(φ/2) cos⁡(πx ‒ 10πt - φ/2)

4)y_result (x,t) = 4 cos⁡(φ/2) sin⁡(2πx ‒ 20πt + φ/2)

5)y_result (x,t) = 2 sin⁡(φ/2) sin⁡(2πx ‒ 20πt + φ/2)

Other:

b)If the amplitude of the resultant wave is A_res = 2 cm, then which of the following values of φ is correct:

1)π/6

2)π/3

3)π/2

4)2π/3

5)π

Other:

c)The speed of the resultant wave due to the interference between y_1 and y_2 is:

1)80π cm/s

2)10 m/s

3)20 m/s

4)80π cos⁡(φ/2) cm/s

5)0.1 m/s

Other:

d)Assume that the two waves start to propagate at the same instant, t_0,1 = t_0,2 = 0 sec, but at different initial positions from an observation point. Wave-1 travels a distance x1 to get to the observation point, while wave-2 travels a distance x2. The amplitude of the resultant wave due to interference would be maximum at the observation point if the path difference between the two waves, ∆x=x2-x1, is:

1)π m

2)4 cm

3)1.5 m

4)0.5 m

5)1 m

Other:

Answer 1