Considering the definition of wavelength, frequency and propagation speed, if the frequency increases by a factor of 4, the wavelength decreases by the same factor.
Wavelength
The wavelength is the minimum distance between two successive points of the wave that are in the same state of vibration. It is expressed in units of length (m).
Frequency
Frequency is the number of vibrations that occur in a unit of time. Its unit is s⁻¹ or hertz (Hz).
Propagation speed
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 disturbance of the wave propagates along its displacement.
Relate the wavelength (λ) and the frequency (f) in an inversely proportional way through the following equation:
v=f×λ
So, the higher the frequency, the shorter the wavelength, and the lower the frequency, the longer the wavelength.
Wavelength in this case
From the expression for the propagation speed, the wavelength can be expressed as:
λ= v÷f1
If the frequency is multiplied by four (f2=4×f1) and being the speed of propagation constant because we are in the same medium, then:
λ= v÷f2
λ= v÷ (4×f1)
λ= [tex]\frac{1}{4}[/tex]× (v÷f1)
In summary, if the frequency increases by a factor of 4, the wavelength decreases by the same factor.
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