Question

The two waves are represented by Y₁ = ${\displaystyle 10-2\sin [50\text{t}+\frac{x}{25}+0.3]}$m and Y₂ = ${\displaystyle {10}^{-2}\cos [50\text{t}+\frac{x}{25}]}$m where x is in metre and time in second. The phase difference between the two waves is nearly _________.

Options

• 1.22 rad

• 1.05 rad

• 1.15 rad

• 1.27 rad

Answer 1

The two waves are represented by Y₁ = ${\displaystyle 10-2\sin [50\text{t}+\frac{x}{25}+0.3]}$m and Y₂ = ${\displaystyle {10}^{-2}\cos [50\text{t}+\frac{x}{25}]}$m where x is in metre and time in second. The phase difference between the two waves is nearly 1.27 rad.

Explanation:

Y₁ = ${\displaystyle 10-2\sin [50\text{t}+\frac{x}{25}+0.3]}$m

Y₂ = ${\displaystyle {10}^{-2}\cos [50\text{t}+\frac{x}{25}]}$m

∴ Phase difference between the two waves is

${\displaystyle \varphi =\frac{\pi }{2}-0.3=1.57-0.3=1.27}$rad