Name: Interference of Waves on a String
Uploaded: 2019-07-19
Duration: 6 min 24 s
Description: Wave interference is the phenomenon that occurs when two waves meet while traveling along the same medium.Here we will study the interference of waves in string. Let's watch.

Question

The ratio of intensities of two waves is

9 : 16

. If these two waves interfere, then determine the ratio of the maximum and minimum possible intensities.

Accepted Answer

Given that the ratio of intensities of two waves is, let $I_{1} : I_{2} = 9 : 16$ .
$\frac{I_{1}}{I_{2}} = \frac{9}{16} (\frac{I_{0}}{I_{0}})$
$\Rightarrow I_{1} = 9 I_{0}$ and $I_{2} = 16 I_{0}$ .
If these two waves interfere, the resultant intensity of the superposed waves is,
$I_{r e s} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} c o s (ϕ)$
If the two waves are in same phase, then the resultant intensity will be maximum.
i.e, $i f ϕ = 0^{o} \Rightarrow \cos (ϕ) = 1$ .
the maximum intensity is,
$I_{m a x} = {(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2} = {(\sqrt{9 I_{0}} + \sqrt{16 I_{0}})}^{2}$
$\Rightarrow I_{m a x} = {(3 \sqrt{I_{0}} + 4 \sqrt{I_{0}})}^{2} = {(7 \sqrt{I_{0}})}^{2} = 49 I_{0}$

If these two waves interfere, the resultant intensity of the superposed waves is,
$I_{r e s} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} c o s (ϕ)$
If the two waves are out of phase, then, the resultant intensity will be minimum.
$i f ϕ = 180^{o} \Rightarrow \cos (ϕ) = - 1$
If these two waves interfere, the minimum intensity is,
$I_{m i n} = {(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2} = {(\sqrt{9 I_{0}} - \sqrt{16 I_{0}})}^{2}$
$\Rightarrow I_{m i n} = {(3 \sqrt{I_{0}} - 4 \sqrt{I_{0}})}^{2} = {(- \sqrt{I_{0}})}^{2} = I_{0}$

The ratio of maximum and minimum possible intensities is,

$\frac{I_{m a x}}{I_{m i n}} = \frac{49 I_{0}}{I_{0}} = \frac{49}{1}$

D. C. Pandey Solutions for Chapter: Superposition of Waves, Exercise 1: INTRODUCTORY EXERCISE 18.1

D. C. Pandey Physics Solutions for Exercise - D. C. Pandey Solutions for Chapter: Superposition of Waves, Exercise 1: INTRODUCTORY EXERCISE 18.1

Questions from D. C. Pandey Solutions for Chapter: Superposition of Waves, Exercise 1: INTRODUCTORY EXERCISE 18.1 with Hints & Solutions

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