Question

An ocean wave has an amplitude of $\mathbf{2}\mathbf{.}\mathbf{5}\mathbf{m}\mathbf{}$. Weather conditions suddenly change such that the wave has an amplitude of$\mathbf{5}.\mathbf{0}\mathbf{m}$. The amount of energy transported by the wave is _____.

• A. halved
• B. doubled
• C. quadrupled
• D. Remains the same

Answer 1

The correct option is C

quadrupled

Step 1 : Given:

Initial Amplitude $\left(A_1\right)$ $=2.5m$

Changed Amplitude $\left(A_2\right)$ $=5.0m$

Step 2: Calculate energy transport:

Energy transport by wave 1 is given as $E_1=k\times {\left(A_{1}f\right)}^2$ where f is the frequency

Energy transport by wave 2 is given as $E_2=k\times {\left(A_{2}f\right)}^2$where f is the frequency

Thus, $\frac{E_2}{E_1}=\frac{k\times {\left(A_{2}f\right)}^2}{k\times {\left(A_{1}f\right)}^2}$

Though the amplitude is changed, the frequency of the wave remains constant.

Therefore, by simplifying the above equation, we get:

$\frac{E_2}{E_1}=\frac{{\left(A_2\right)}^2}{{\left(A_1\right)}^2}$

Substituting given values:

$\frac{E_2}{E_1}=\frac{{\left(5.0\right)}^2}{{\left(2.5\right)}^2}$

Solving the above expression, we get:

$\frac{E_2}{E_1}=4$

$\Rightarrow E_2=4E_1$

Thus, the energy transported by the wave with changed amplitude is four times or quadrupled the initial energy.

Hence, Option (c) is the correct answer.