The superposing waves are represented by the following equations y1=5 sin 2 π(10 t-0.1 x), y2=10 sin 2 π(20 t-0.2 x) Ratio of intensities (I max /I min ) will be:

Question

The superposing waves are represented by the following equations y1=5 sin 2 π(10 t-0.1 x), y2=10 sin 2 π(20 t-0.2 x) Ratio of intensities (I max /I min ) will be: (A) 1 (B) 9 (C) 4 (D) 16

Tardigrade Admin · Accepted Answer

Given that a1=5, a2=10 ⇒ (I max /I min )=((a1+a2)2/(a1-a2)2) =((5+10/5-10))2=(9/1).

Q. The superposing waves are represented by the following equations
$y_{1} = 5 sin 2 π (10 t - 0.1 x), y_{2} = 10 sin 2 π (20 t - 0.2 x)$ Ratio of intensities $\frac{I _{m a x}}{I _{m i n}}$ will be:

1

9

4

16

Given that
$a_{1} = 5, a_{2} = 10$
$\Rightarrow \frac{I _{m a x}}{I _{m i n}} = \frac{( a _{1} + a _{2} ) ^{2}}{( a _{1} - a _{2} ) ^{2}}$
$= (\frac{5 + 10}{5 - 10})^{2} = \frac{9}{1}$ .

Q. The superposing waves are represented by the following equations y1​=5sin2π(10t−0.1x),y2​=10sin2π(20t−0.2x) Ratio of intensities Imin​Imax​​ will be:

1

9

4

16

Given that a1​=5,a2​=10 ⇒Imin​Imax​​=(a1​−a2​)2(a1​+a2​)2​ =(5−105+10​)2=19​.

Q. The superposing waves are represented by the following equations
$y_{1} = 5 sin 2 π (10 t - 0.1 x), y_{2} = 10 sin 2 π (20 t - 0.2 x)$ Ratio of intensities $\frac{I _{m a x}}{I _{m i n}}$ will be:

Given that
$a_{1} = 5, a_{2} = 10$
$\Rightarrow \frac{I _{m a x}}{I _{m i n}} = \frac{( a _{1} + a _{2} ) ^{2}}{( a _{1} - a _{2} ) ^{2}}$
$= (\frac{5 + 10}{5 - 10})^{2} = \frac{9}{1}$ .