A wave is introduced into a thin wire held tight at each end. It has an amplitude of $3.8 c m$ , a frequency of $51.2 H z$ and a distance from a crest to the neighbouring trough of $12.8 c m$ . Determine the period of such a wave.

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Solution

Step1: Given Data
The amplitude of the wave, $A = 3.8 c m$
Frequency, $f = 51.2 H z$
Distance from a crest to the neighboring trough, $d = 12.8 c m$
Step2: Determine the period
The period $(T)$ of a wave is the time taken by the wave to complete a full cycle.
The frequency $(f)$ of a wave is the number of complete cycles a wave make in unit time.
The period and frequency of a wave are related by the following equation:
$T = \frac{1}{f}$
Putting $f = 51.2 H z$ in the above equation:
$T = \frac{1}{51.2} s$
$= 0.019 s$

Hence, the period of the given wave is $0.019 s$ .

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A wave is introduced into a thin wire held tight at each end. It has an amplitude of 3.8cm, a frequency of 51.2Hz and a distance from a crest to the neighbouring trough of 12.8cm. Determine the period of such a wave.

A wave is introduced into a thin wire held tight at each end. It has an amplitude of $3.8 c m$ , a frequency of $51.2 H z$ and a distance from a crest to the neighbouring trough of $12.8 c m$ . Determine the period of such a wave.