What variables must be known to determine the observed frequency of a wave?

The frequency, 'f', of a wave is given by the speed, 'v' of the wave and the wavelength, λ, of the wave

f = v/λ

The frequency, 'f', of a wave is also given by the inverse of the period, 'T', of the wave which is the time it takes the wave to complete an oscillation or a cycle

f 1/T

Therefore, the variables to be known to determine the frequency of a wave includes either, the velocity and the wavelength of the wave or the period of oscillation (the wave cycle) of the wave

Explanation:

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