SATHEE: Waves - Result Question 2

Waves - Result Question 2

2. Two waves are represented by the equations $y_{1} = a \sin (ω t + k x + 0.57) m$ and $y_{2} = a \cos (ω t$ $+ k x) m$ , where $x$ is in meter and $t$ in sec. The phase difference between them is [2011]

(a) 1.0 radian

(b) 1.25 radian

(d) 0.57 radian

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Answer:

Correct Answer: 2. (a)

Solution:

(a) Here, $y_{1} = a \sin (ω t + k x + 0.57)$

so, $ϕ_{1} = 0.57$

and $y_{2} = a \cos (ω t + k x)$

$= a \sin [\frac{π}{2} + (ω t + k x)]$

so, $ϕ_{2} = π / 2$

Phase difference, $Δ ϕ = ϕ_{2} - ϕ_{1}$

$\begin{matrix} = \frac{π}{2} - 0.57 = \frac{3.14}{2} - 0.57 = 1.57 - 0.57 \\ = 1 radian \end{matrix}$

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Waves - Result Question 2

2. Two waves are represented by the equations y1=asin⁡(ωt+kx+0.57)m and y2=acos⁡(ωt +kx)m, where x is in meter and t in sec. The phase difference between them is [2011]

Answer:

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2. Two waves are represented by the equations $y_{1} = a \sin (ω t + k x + 0.57) m$ and $y_{2} = a \cos (ω t$ $+ k x) m$ , where $x$ is in meter and $t$ in sec. The phase difference between them is [2011]