To determine the period of a wave, you need to understand the relationship between frequency and period. The period of a wave is defined as the reciprocal of its frequency. Mathematically, this relationship is given by:
[tex]\[ T = \frac{1}{f} \][/tex]
where [tex]\( T \)[/tex] is the period and [tex]\( f \)[/tex] is the frequency.
Given that the frequency [tex]\( f \)[/tex] of the wave is 256 cycles per second (Hz), we can substitute this value into the formula to find the period [tex]\( T \)[/tex].
[tex]\[ T = \frac{1}{256} \text{ seconds} \][/tex]
When calculating this, we obtain:
[tex]\[ T = 0.00390625 \text{ seconds} \][/tex]
Therefore, the period of the wave is 0.00390625 seconds.
Looking at the given options:
A) 1s
B) 1/256 s
C) 256 s
D) 512 s
We see that option B) 1/256 s is the correct answer, as:
[tex]\[ \frac{1}{256} \text{ seconds} \][/tex]
is equal to 0.00390625 seconds.
