Sure, let's solve this step by step.
1. Convert the crest-to-crest length from centimeters to millimeters:
- Given length is 6 centimeters.
- Since 1 centimeter equals 10 millimeters, the length in millimeters is:
[tex]\[
6 \, \text{cm} \times 10 = 60 \, \text{mm}
\][/tex]
2. Calculate the time for one cycle (crest-to-crest distance) using the time base:
- The time base is given as 25 centiseconds per millimeter.
- To find the total time for the signal to cover the crest-to-crest distance, multiply the length in millimeters by the time base:
[tex]\[
60 \, \text{mm} \times 25 \, \text{cs/mm} = 1500 \, \text{centiseconds}
\][/tex]
3. Convert the time from centiseconds to seconds:
- Since 1 centisecond is equal to 0.01 seconds, convert 1500 centiseconds to seconds:
[tex]\[
1500 \, \text{cs} \times 0.01 = 15.0 \, \text{seconds}
\][/tex]
4. Determine the frequency of the signal:
- Frequency is the reciprocal of the period (time for one complete cycle). Thus, frequency [tex]\(f\)[/tex] is given by:
[tex]\[
f = \frac{1}{T}
\][/tex]
where [tex]\( T \)[/tex] is the period in seconds.
- Hence, the frequency is:
[tex]\[
f = \frac{1}{15.0 \, \text{seconds}} = 0.06666666666666667 \, \text{Hz}
\][/tex]
Therefore, the frequency of the signal is approximately [tex]\(0.067 \, \text{Hz}\)[/tex].
