Taking into account the definition of wavelength, frecuency and propagation speed, the frecuency of a wave with a wavelength of 4.257×10⁻⁷ cm is 7.05×10¹⁶ Hz.
First of all, in a periodic wave the wavelength is the physical distance between two points from which the wave repeats itself. In other words, the wavelength is the distance that separates a certain point of a periodic phenomenon from the next point with the same characteristics. 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. The propagation speed of a sound wave depends on the characteristics of the medium in which the propagation occurs and not on the characteristics of the wave or the force that generates it.
The propagation speed relate the wavelength (λ) and the frequency (f) inversely proportional using the following expression:
v = f * λ
All electromagnetic waves propagate in a vacuum at a constant speed of 3x10⁸ m/s, the speed of light.
In this case, you know:
Replacing:
3x 10⁸ m/s= f × 4.257×10⁻⁹ m
Solving:
f= 3x 10⁸ m/s ÷ 4.257×10⁻⁹ m
f= 7.05×10¹⁶ Hz
In summary, the frecuency of a wave with a wavelength of 4.257×10⁻⁷ cm is 7.05×10¹⁶ Hz.
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