Q: The two waves are represented by :

y_{1} = 10^{-6} sin(100t + x/50 + 0.5) m

and y_{2} = 10^{-2} cos(100t + x/50) m

where x is in metres and t in seconds. The phase difference between the waves is approximately:

(a) 1.07 rad

(b) 2.07 rad

(c) 0.5 rad

(d) 1.5 rad

Ans: (a)

**Solution :** y_{1} = 10^{-6} sin(100t + x/50 + 0.5)m

and y_{2} = 10^{-2} sin(100t + x/50 + π/2)m

y_{2} = 10^{-2} sin(100t + x/50 + 1.57 )m

Phase difference = (100 t + x/50 + 1.57 ) – (100 t + x/50 + 0.5 )

= 1.07 rad

#### Also Read :

- An alternating voltage E = 200√2 sin (100t) volt is connected to a 1μF capacitor through an…
- Two waves are represented by : y1 = a1 cos (ωt – kx) and y2 = a2 sin(ωt – kx + π/3)....
- A wave is represented by y = a sin (At –Bx + C), where A, B, C are constant. The dimensions…
- In a region, the potential is represented by V(x,y,z)=6 x-8xy-8 y + 6 yz, where V is in volt…
- A physical quantity is represented by x=M^a L^b T^(-c). The percentage of errors in the…
- If the position of a particle along Y axis is represented as a function of time t by the…
- A virtual erect image in a concave mirror is represented, in the above figures,
- A reflected surface is represented by the equation y = 2L/π sin(πx/L) , 0 ≤ x ≤ L . A ray…
- If the voltage in an ac circuit is represented by the equation. V = 220√2sin (314t - φ) volt…
- Which of the following options is correct for the object having a straight line motion…