To determine whether the statement "The frequency of this wave is 1/5 seconds" is true or false, we need to understand the concepts of period and frequency.
1. Period (T): The period is the time it takes for one complete cycle of the wave. In this context, the period is given as 5 seconds, meaning a point on the wave completes one cycle every 5 seconds.
2. Frequency (f): Frequency is the number of cycles the wave completes in one second. It is the reciprocal of the period. The formula for frequency is:
[tex]\[
f = \frac{1}{T}
\][/tex]
Given that the period [tex]\( T \)[/tex] is 5 seconds, we can calculate the frequency as follows:
[tex]\[
f = \frac{1}{5 \text{ seconds}}
\][/tex]
This calculation gives a frequency of:
[tex]\[
f = 0.2 \text{ Hz (Hertz)}
\][/tex]
The frequency of the wave is 0.2 Hz, which means the wave completes 0.2 cycles per second.
Now, let's examine the statement: "The frequency of this wave is 1/5 seconds."
1/5 seconds is the same as 0.2 Hz. Therefore, the statement correctly describes the frequency of the wave.
Hence, the statement is:
True
