To solve the problem of determining the frequency of a wave with a period of 18 seconds, we need to use the relationship between period and frequency. The frequency [tex]\( f \)[/tex] is the inverse of the period [tex]\( T \)[/tex]. This relationship can be expressed with the following formula:
[tex]\[ f = \frac{1}{T} \][/tex]
Given:
- Period [tex]\( T = 18 \)[/tex] seconds
Using the formula:
[tex]\[ f = \frac{1}{18} \][/tex]
Now we must calculate [tex]\( \frac{1}{18} \)[/tex]. Performing this division gives:
[tex]\[ \frac{1}{18} \approx 0.055555... \][/tex]
We can express this result in scientific notation. To do this:
[tex]\[ 0.055555... \approx 5.555 \times 10^{-2} \][/tex]
Next, we look at the provided options to find the closest match:
A. [tex]\( 6.6 \times 10^{-2} \)[/tex] hertz
B. [tex]\( 5.5 \times 10^{-2} \)[/tex] hertz
C. [tex]\( 3.3 \times 10^{-2} \)[/tex] hertz
D. [tex]\( 1.8 \times 10^{-2} \)[/tex] hertz
E. [tex]\( 8.0 \times 10^{-3} \)[/tex] hertz
In comparison, the closest value to [tex]\( 5.555 \times 10^{-2} \)[/tex] hertz is clearly:
B. [tex]\( 5.5 \times 10^{-2} \)[/tex] hertz
Therefore, the correct answer is:
[tex]\[ \boxed{5.5 \times 10^{-2} \text{ hertz}} \][/tex]
