Question

the data given shows the amplitude and energy of several simple waves. amplitude of wave (cm) energy of wave (j) 0.5 1.0 1.0 4.0 1.5 9.0 based on the data, what should be the amount of energy for a simple wave with an amplitude of 3.0 cm? a. 12.0 j b. 16.0 j c. 18.0 j d. 36.0 j

Explanation:

Step1: Observe the relationship

Notice that when amplitude $A = 0.5$, energy $E=1.0$; when $A = 1.0$, $E = 4.0$; when $A=1.5$, $E = 9.0$. The relationship between energy $E$ and amplitude $A$ seems to be $E = kA^{2}$. Substituting $A = 0.5$ and $E = 1.0$ into $E=kA^{2}$, we get $1.0=k\times(0.5)^{2}$, so $k=\frac{1.0}{0.25}=4$.

Step2: Calculate energy for $A = 3.0$

Using the formula $E = 4A^{2}$, when $A = 3.0$ cm, $E=4\times(3.0)^{2}=4\times9 = 36.0$ J.

Answer:

D. 36.0 J