Question

If amplitude is 200, intensity is 300. When amplitude is increased to 800 then
what will be intensity?
(A)1200
(B)1400
(C)1600
(D) 1800​

Answer 1

Given:

Initial amplitude $\rm (A_i)$ = 200

Initial intensity $\rm (I_i)$ = 300

Final amplitude $\rm (A_f)$ = 800

To Find:

Final intensity $\rm (I_f)$

Answer:

Intensity of wave is directly proportional to amplitude square i.e.

$\boxed{ \bf{I \propto A^2}}$

So,

$\rm \implies \dfrac{I_i}{I_f} = \dfrac{{A_i}^{2}}{{A_f}^{2}} \\ \\ \rm \implies \dfrac{300}{I_f} = \dfrac{{200}^{2}}{{800}^{2}} \\ \\ \rm \implies \dfrac{300}{I_f} = {(\dfrac{200}{800}) }^{2} \\ \\ \rm \implies \dfrac{300}{I_f} = {(\dfrac{1}{4}) }^{2} \\ \\ \rm \implies \dfrac{300}{I_f} =\dfrac{1}{16} \\ \\ \rm \implies I_f = 4800$

$\therefore$ $\boxed{\mathfrak{Final \ intensity \ (I_f) = 4800}}$

Answer 2

$\bigstar$ Given

If amplitude is 200, intensity is 300. When amplitude is increased to 800

$\bigstar$ To Find

Find new intensity

$\bigstar$ Solution

We know that

The intensity of a wave is directly proportional to the square of its amplitude

Mathematically

$\red{\rm \longrightarrow I \propto a^{2}}$

Here

• I = intensity
• a = amplitude

According to the question

We are asked to find the new intensity

Given that

If amplitude is 200, intensity is 300. When amplitude is increased to 800

Hence

• I = 300
• a = 200
• a' = 800

Increase in amplitude (A)

$\blue{\rm \longrightarrow A=\dfrac{a^{'}}{a}}$

Hence

$\green{\rm \longrightarrow A= \dfrac{800}{200}}$

On further simplification

We get

$\orange{\rm \longrightarrow A= 4}$

Increase in amplitude (squared)

Therefore

$\pink{\rm \longrightarrow A^{2}= 4^{2}}$

Hence

$\red{\rm \longrightarrow A^{2}= 16}$

Therefore

Amplitude squared increases by a factor of 16

Hence

$\orange{\rm \longrightarrow I^{'}=I \times A^{2}}$

Here

• I' = new intensity
• I = initial intensity
• A² = squared amplitude factor

Given that

If amplitude is 200, intensity is 300. When amplitude is increased to 800

Hence

• I = 300

We found out that

• A² = 16

Substituting the values

We get

$\blue{\rm \longrightarrow I^{'}=300 \times 16}$

On further simplification

We get

$\green{\rm \longrightarrow I^{'}=4800}$

Hence

$\checkmark$ New intensity = 4800

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Therefore

When amplitude is increased to 800 then intensity will be 4800