Three harmonic waves having equal frequency v and same intensity I0, have phase angles 0, (π/4) and -(π/4) When they are superimposed the intensity of the resultant wave is close to :

Question

Three harmonic waves having equal frequency v and same intensity I0, have phase angles 0, (π/4) and -(π/4) When they are superimposed the intensity of the resultant wave is close to : (A) 0.2 I0 (B) I0 (C) 3 I0 (D) 5.8 I0

Tardigrade Admin · Accepted Answer

=A sin ω t+A sin(ω t-(π/4))+A sin(ω t+(π /4)) =A sin ω t+√2 =A sin ω t =(√2+1)=A sin ω t Resultant wave amplitude =(√2+1)A as I propto A2 so (I/I0)=(√2+1)2 I=5.8 I0

Q. Three harmonic waves having equal frequency v and same intensity $I_{0}$ , have phase angles $0, \frac{π}{4}$ and $- \frac{π}{4}$ When they are superimposed the intensity of the resultant wave is close to :

$0.2 I_{0}$

$I_{0}$

$3 I_{0}$

$5.8 I_{0}$

$= A s in ω t + A s in (ω t - \frac{π}{4}) + A s in (ω t + \frac{π}{4})$
$= A s in ω t + 2 = A s in ω t$
$= (2 + 1) = A s in ω t$
Resultant wave amplitude $= (2 + 1) A < b r / > a s I \propto A^{2}$
so $\frac{I}{I _{0}} = (2 + 1)^{2}$
$I = 5.8 I_{0}$

Q. Three harmonic waves having equal frequency v and same intensity I0​, have phase angles 0,4π​ and −4π​ When they are superimposed the intensity of the resultant wave is close to :

0.2I0​

I0​

3I0​

5.8I0​