A stone thrown into still water, creates a circular wave pattern moving radially outwards. If, r is the distance measured from the centre of the pattern, the amplitude of the wave varies as

Question

A stone thrown into still water, creates a circular wave pattern moving radially outwards. If, r is the distance measured from the centre of the pattern, the amplitude of the wave varies as (A) r-3 / 2 (B) (r-1 / 2/2) (C) r-1 (D) r1 / 3

Tardigrade Admin · Accepted Answer

As, I(=(P/4 π r2)) propto A2 ⇒ A propto (1/r)

Q. A stone thrown into still water, creates a circular wave pattern moving radially outwards. If, $r$ is the distance measured from the centre of the pattern, the amplitude of the wave varies as

$r^{- 3/2}$

$\frac{r ^{- 1/2}}{2}$

$r^{- 1}$

$r^{1/3}$

As, $I (= \frac{P}{4 π r ^{2}}) \propto A^{2}$
$\Rightarrow A \propto \frac{1}{r}$

Q. A stone thrown into still water, creates a circular wave pattern moving radially outwards. If, r is the distance measured from the centre of the pattern, the amplitude of the wave varies as

r−3/2

2r−1/2​

r−1

r1/3