Question

from a line source ,if amplitude of a wave at a distance r is A , then the amplitude at a distance 4r will be?

Answer 1

Answer: The amplitude will be A = $\dfrac{A}{4}$.

Explanation:

Given that,

Amplitude = A

Distance = r

We know that,

Intensity is inversely proportional to the square of the distance.

$I\propto \dfrac{1}{r^{2}}$

We know that,

$I = A^{2}$

So, $A^{2}\propto \dfrac{1}{r^{2}}$

$A\propto \dfrac{1}{r}$...(I)

Now, put the distance r = 4r in equation (I)

$A'\propto \dfrac{1}{4r}$...(II)

Now, taking the ratio of equation(II) and (I)

$\dfrac{A'}{A} = \dfrac{r}{4r}$

$A' = \dfrac{A}{4}$

Hence, the amplitude at a distance 4r will be A = $\dfrac{A}{4}$.