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The frequency of a wave is defined as the number of complete wave cycles passing a given point per unit of time. To calculate the frequency, we need to determine the time it takes for one complete wave cycle to pass a given point.
The distance between two successive crests is called the wavelength (λ). In this case, the wavelength is given as 38 cm, but we need to convert it to meters to maintain consistent units:
Wavelength (λ) = 38 cm = 0.38 m
The speed of the wave is given as 4.2 m/s, which represents the distance the wave travels in one second. Therefore, we can use the formula:
Speed (v) = Frequency (f) × Wavelength (λ)
Rearranging the formula to solve for frequency, we get:
Frequency (f) = Speed (v) / Wavelength (λ)
Substituting the given values:
Frequency (f) = 4.2 m/s / 0.38 m ≈ 11.05 Hz
Therefore, the frequency of the wave is approximately 11.05 Hz.
