Question

Wave 1 displaces according the function f(θ)= 2sin θ+1. Wave 2 displaces according to the function f(θ)= 3sin θ+.5. At what angle, in degrees, will the two waves have the same displacement?

Answer 1

Answer:

θ = 30⁰  

Explanation:

We have been given two wave displacement equations,

$y_{1} =2sin\theta +1$     ........(1)

$y_{2}=3sin\theta +0.5$     ........(2)

The waves will have same displacements when $y_{1}=y_{2}=y$ (say)

Therefore, operating (2) - (1), we get,

$sin\theta - 0.5=0$

or, $\theta = sin^{-1}(0.5)=30^{o}$ (since, sin 30⁰ = 0.5)

We can check the answer by putting $\theta=30^{o}$ in equations (1) and (2),

$y_{1}=2sin30^{o}+1=2\times0.5 + 1= 2$

$y_{2}=3sin30^{o}+0.5=3\times0.5+0.5=1.5+0.5=2$

Answer 2

Answer:

θ= 30°

Explanation:

Set the wave functions equal to another, as displacements would be the same. Therefore, 2sin θ+1 = 3sin θ+.5.

sin θ=.5

θ= 30°