Following transverse waves, y1=2 sin (100 π t-5.3 x) , y2=2 √2 sin (100-5.3 x+(π/4)) and y3= sin (100 π t-5.3 x) superpose in a homogenous medium. Find the resultant amplitude at x=0.

Question

Following transverse waves, y1=2 sin (100 π t-5.3 x) , y2=2 √2 sin (100-5.3 x+(π/4)) and y3= sin (100 π t-5.3 x) superpose in a homogenous medium. Find the resultant amplitude at x=0. (A) 1 unit (B) 4 unit (C) 5 unit (D) 2 unit

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/bd39bb88dc5f371af599381dd8a0d0f2-.png" /> Here, ax =2+2 √2 cos (π/4) =4 unit ay =2 √2 sin 45°+1 =3 unit A =√Ax2+ay2 =√42+32=5 unit

Q. Following transverse waves,
$y_{1} = 2 sin (100 π t - 5.3 x)$ ,
$y_{2} = 22 sin (100 - 5.3 x + \frac{π}{4})$
and $y_{3} = sin (100 π t - 5.3 x)$
superpose in a homogenous medium. Find the resultant amplitude at $x = 0$ .

1 unit

4 unit

5 unit

2 unit

Here,
$a_{x} = 2 + 22 cos \frac{π}{4}$
$= 4$ unit
$a_{y} = 22 sin 4 5^{\circ} + 1$
$= 3$ unit
$A = A_{x}^{2} + a_{y}^{2}$
$= 4^{2} + 3^{2} = 5$ unit

Q. Following transverse waves, y1​=2sin(100πt−5.3x), y2​=22​sin(100−5.3x+4π​) and y3​=sin(100πt−5.3x) superpose in a homogenous medium. Find the resultant amplitude at x=0.