To analyze the relationship between the amplitude and energy of a mechanical wave, let's look at the provided data table, which shows the energy associated with different amplitudes:
[tex]\[
\begin{array}{|l|l|}
\hline
\text{Amplitude} & \text{Energy} \\
\hline
1 \, \text{unit} & 2 \, \text{units} \\
\hline
2 \, \text{units} & 8 \, \text{units} \\
\hline
3 \, \text{units} & 18 \, \text{units} \\
\hline
4 \, \text{units} & 32 \, \text{units} \\
\hline
5 \, \text{units} & 50 \, \text{units} \\
\hline
\end{array}
\][/tex]
For mechanical wave [tex]\( A \)[/tex] with an amplitude of 4 cm:
- From the table, the energy corresponding to an amplitude of 4 units is 32 units.
For mechanical wave [tex]\( B \)[/tex] with an amplitude of 5 cm:
- From the table, the energy corresponding to an amplitude of 5 units is 50 units.
Next, we find the ratio of the energies carried by waves [tex]\( B \)[/tex] and [tex]\( A \)[/tex]:
[tex]\[
\text{Energy ratio} = \frac{\text{Energy of wave } B}{\text{Energy of wave } A} = \frac{50}{32} = 1.5625
\][/tex]
This tells us that wave [tex]\( B \)[/tex] carries about 1.5625 times more energy than wave [tex]\( A \)[/tex].
Given the options:
A. Wave A has about 1.15 times more energy than wave [tex]\( B \)[/tex].
B. Wave B has about 1.6 times more energy than wave [tex]\( A \)[/tex].
C. Wave A has about 1.25 times more energy than wave [tex]\( B \)[/tex].
D. Wave A has about 1.6 times more energy than wave [tex]\( B \)[/tex].
The correct option is:
B. Wave B has about 1.6 times more energy than wave [tex]\( A \)[/tex].
