To analyze the relationship between the amplitude and energy of a mechanical wave, let's take a look at the provided data:
[tex]\[
\begin{array}{|c|c|}
\hline \text{Amplitude (units)} & \text{Energy (units)} \\
\hline 1 & 2 \\
\hline 2 & 8 \\
\hline 3 & 18 \\
\hline 4 & 32 \\
\hline 5 & 50 \\
\hline
\end{array}
\][/tex]
We are given the amplitudes for waves [tex]\( A \)[/tex] and [tex]\( B \)[/tex] as follows:
- Wave [tex]\( A \)[/tex] has an amplitude of 4 units.
- Wave [tex]\( B \)[/tex] has an amplitude of 5 units.
Using the provided data, we can identify the energy corresponding to these amplitudes:
- For wave [tex]\( A \)[/tex] with an amplitude of 4 units, the energy is 32 units.
- For wave [tex]\( B \)[/tex] with an amplitude of 5 units, the energy is 50 units.
Next, we need to find the ratio of the energy of wave [tex]\( B \)[/tex] to the energy of wave [tex]\( A \)[/tex]:
[tex]\[
\text{Ratio of energy}\, B \text{ to energy}\, A = \frac{\text{Energy of } B}{\text{Energy of } A} = \frac{50}{32} = 1.5625
\][/tex]
Interpreting this ratio:
- Wave [tex]\( B \)[/tex] has [tex]\( 1.5625 \)[/tex] times more energy than wave [tex]\( A \)[/tex].
Thus, the correct choice is:
B. Wave [tex]\( B \)[/tex] has about 1.6 times more energy than wave [tex]\( A \)[/tex].
So, the answer to the question is:
B. Wave [tex]\( B \)[/tex] has about 1.6 times more energy than wave [tex]\( A \)[/tex].
