Question

Choose the correct option for the given assertion and reason.

Assertion : When a wave travels from a denser medium to rarer medium, its amplitude of oscillation increases.

Reason : In denser medium, speed of wave is less compared to that in rarer medium.

• A. Assertion and Reason both are true and the Reason is correct explanation of the Assertion.
• B. Assertion and Reason both are true, but Reason is not the correct explantion of Assertion.
• C. Assertion is true, but Reason is false
• D. Assertion is false, but Reason is true.

Answer 1

The correct option is A Assertion and Reason both are true and the Reason is correct explanation of the Assertion.

Velocity of a wave on a string is given as $\left(v\right)=\sqrt{\frac{T}{\mu }}$
where $T\to$ Tension in the string
$\mu \to$ Linear density of the medium.

i.e $v\propto \frac{1}{\sqrt{\mu }}.......\left(1\right)$

Let the linear density of the denser medium be ${\mu }_1$ and of the rarer medium be ${\mu }_2$.
$\therefore$ From $\left(1\right)$, we can conclude that, $v_1<v_2$
$v_1\to$ velocity of wave in denser medium
$v_2\to$ velocity of wave in rarer medium

Now, if amplitude of the transmitted wave is $A_t$,
$A_t=\left(\frac{2v_2}{v_1+v_2}\right)A_i$
$v_1<v_2\Rightarrow v_1+v_2<2v_2$
so, $A_t>A_i$

Hence option (a) is the correct answer.