Question

question 5 of 10
the data table shows how the amplitude of a mechanical wave varies with the energy it carries. analyze the data to identify the mathematical relationship between amplitude and energy. use your equation to find the energy if the amplitude is 9 units.

amplitude	energy
2 units	8 units
3 units	18 units
4 units	32 units

a. 98 units
b. 162 units
c. 324 units
d. 54 units

Explanation:

Step1: Identify the relationship

Let the amplitude be $A$ and energy be $E$. By observing the data: when $A = 1$, $E=2\times1^{2}$; when $A = 2$, $E = 2\times2^{2}=8$; when $A=3$, $E=2\times3^{2}=18$; when $A = 4$, $E=2\times4^{2}=32$. The relationship is $E = 2A^{2}$.

Step2: Calculate the energy for $A = 9$

Substitute $A = 9$ into the equation $E = 2A^{2}$. Then $E=2\times9^{2}=2\times81 = 162$.

Answer:

C. 324 units