Solve 13 and explain in english as the answer given in thebook is 50Hz

The time period ($T$) of a wave is the time taken for one complete oscillation or cycle.
Looking at the displacement-time graph:

• The wave starts at zero displacement at time $t = 0$.
• It moves upwards to a positive peak, then crosses the zero displacement line at $t = 0.01$ s. This marks half a cycle.
• It then moves downwards to a negative trough and returns to the zero displacement line at $t = 0.02$ s, completing one full cycle (one crest and one trough). Therefore, the time period of the wave is $T = 0.02$ seconds.

The frequency ($f$) of a wave is the reciprocal of its time period ($T$). The formula is:

$$f = \frac{1}{T}$$

Substitute $T = 0.02$ s into the formula:

$$f = \frac{1}{0.02 \text{ s}}$$ $$f = \frac{1}{\frac{2}{100}} \text{ Hz}$$ $$f = \frac{100}{2} \text{ Hz}$$ $$f = 50 \text{ Hz}$$

The calculated frequency is 50 Hz, which corresponds to option (a).

The frequency of the wave is:

(a) $\text{50 Hz}$