Taking into account the definition of wavelength, frecuency and propagation speed, the wavelength of a wave at a speed of 3×10⁸ m/s and has a frequency of 1.5×10¹⁶ Hz is 2×10⁻⁸ m.
Wavelength is the minimum distance between two successive points on the wave that are in the same state of vibration. It is expressed in units of length (m).
On the other side, frequency is the number of vibrations that occur in a unit of time. Its unit is s⁻¹ or hertz (Hz).
Finally, the propagation speed is the speed with which the wave propagates in the medium, that is, it is the magnitude that measures the speed at which the wave disturbance propagates along its displacement.
The propagation speed relate the wavelength (λ) and the frequency (f) inversely proportional using the following equation:
v = f× λ
All electromagnetic waves propagate in a vacuum at a constant speed of 3×10⁸ m/s, the speed of light.
In this case, you know:
Replacing in the expression for the propagation speed:
3×10⁸ m/s= 1.5×10¹⁶ Hz× λ
Solving:
λ= 3×10⁸ m/s ÷ 1.5×10¹⁶ Hz
λ= 2×10⁻⁸ m
In summary, the wavelength of a wave at a speed of 3×10⁸ m/s and has a frequency of 1.5×10¹⁶ Hz is 2×10⁻⁸ m.
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