Derive the formula for the speed of waves () relating speed, frequency, and wavelength.

The formula for wave speed can be derived from the wave equation:

v = fλ

Where:

– v is the wave speed (in meters per second)

– f is the frequency (in hertz)

– λ is the wavelength (in meters)

The wave equation describes the relationship between the wavelength, frequency, and wave speed for any type of wave, including electromagnetic waves and mechanical waves.

To derive this formula, we can start with the definition of wave speed:

v = distance traveled by wave / time taken

For a wave, the distance traveled in one period (T) is equal to the wavelength (λ), so we can substitute this into the equation:

v = λ / T

But the frequency (f) is defined as the number of cycles (or periods) per second, so we can substitute f for 1/T:

v = fλ

Thus, we have derived the formula for wave speed, v = fλ.

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