Answer – The period of a wave can be found using a modified version of the wave equation, $T = \lambda / v$. For the given wave, it is found to be 0.714 s.

Explanation:

To know how to find the period of a wave, we need to review what it is with its related terms. 

The period of a wave, indicated by T, is the duration of a complete wave cycle. Its frequency (f) is the number of cycles the wave completes in one second. Thus, frequency is the inverse of the period of a wave and vice versa.

So the formula for the frequency of a wave is:

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

And the formula for the time period of a wave is:

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

Further, the distance that a wave moves in one period is known as its wavelength, represented by $\lambda$.

Since the given question provides us with the values of wavelength and speed, we can use all the above information with respect to a wave in the equation Speed (v) = Distance / Time:

$v = \frac{\lambda }{T}$

$v = \lambda \times \frac{1}{T}$

$v = \lambda \times f$

$v = f \lambda$

This is the wave equation, which represents the relationship between the speed of a wave, its frequency, and its wavelength.

Since the given question requires us to find the period of the given wave, the wave equation can be modified as follows:

$v = \frac{\lambda }{T}$

$T = \frac{\lambda }{v}$

Substituting $\lambda$ = 5 m and v = 7 m/s from the question in the above equation, we get:

$T = \frac{5 m}{7 m/s}$

$T = 0.714 s$

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