Sure, let's go through the detailed, step-by-step solution for finding the frequency of a wave given that its period is 18 seconds.
1. Understanding the relationship:
Frequency ([tex]\(f\)[/tex]) and period ([tex]\(T\)[/tex]) of a wave are related by the formula:
[tex]\[
f = \frac{1}{T}
\][/tex]
where:
- [tex]\(f\)[/tex] is the frequency in hertz (Hz)
- [tex]\(T\)[/tex] is the period in seconds
2. Plug in the given period:
The given period [tex]\(T\)[/tex] is 18 seconds.
So we can find the frequency using:
[tex]\[
f = \frac{1}{18} \text{ Hz}
\][/tex]
3. Calculate the frequency:
Performing the division:
[tex]\[
f = \frac{1}{18} \approx 0.05555555555555555 \text{ Hz}
\][/tex]
4. Convert the frequency to scientific notation:
The numerical value 0.05555555555555555 can be expressed in scientific notation. We find the closest standard form:
[tex]\[
0.05555555555555555 \approx 5.555555555555555 \times 10^{-2} \text{ Hz}
\][/tex]
To match with the given answer choices, it’s rounded up to one decimal place in scientific notation:
[tex]\[
5.6 \times 10^{-2} \text{ Hz}
\][/tex]
5. Match the result with the given answer choices:
Comparing the calculated frequency [tex]\(0.05555555555555555\)[/tex] Hz, the answer that corresponds to it is [tex]\(5.5 \times 10^{-2} \text{ Hz}\)[/tex].
Thus, the correct answer is:
B. [tex]\(5.5 \times 10^{-2} \text{ hertz}\)[/tex]
