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How does the wavelength of a light wave change if the frequency is increased
by a factor of 3? Assume the speed of the wave remains unchanged.
O A. The wavelength decreases by a factor of 3.
B. The wavelength does not change.
O C. The wavelength increases by a factor of 3.
D. The wavelength increases by a factor of 9.

Sagot :

MDKPfromIDN

(A). The wavelength decreases by a factor of 3.

Introduction :

Hi ! We all know that all type of electromagnetic wave, will have the same velocity as the speed of light, because light is part of electromagnetic wave too. The value of it is 300,000 km/s or [tex] \sf{3 \times 10^8} [/tex] m/s. As a result of this constant property, the shorter the wavelength, the greater the value of the electromagnetic wave frequency. This relationship can also be expressed in this equation:

[tex] \boxed{\sf{\bold{c = \lambda \times f}}} [/tex]

With the following condition :

  • c = the constant of the speed of light in a vacuum ≈ [tex] \sf{3 \times 10^{8} \: m/s} [/tex] m/s
  • [tex] \sf{\lambda} [/tex] = wavelength (m)
  • f = electromagnetic wave frequency (Hz)

Explanation

In this problem, we underline one concept, namely : "the shorter the wavelength, the greater the value of the electromagnetic wave frequency". In question, the frequency of the waveform will increase by a factor of 3 from the beginning. So, to keep this value constant, the wavelength should be reduced by a factor of 3 from the initial condition.

Proof

Assume that:

  • c = c' = speed of the electromagnetic wave is always the same (constant).
  • [tex] \sf{\lambda} [/tex] = initial wavelength = [tex] \sf{\lambda} [/tex]
  • f = initial frequency = f
  • f' = final frequency = 3f

Let we count :

  • [tex] \sf{\lambda}' [/tex] = final wavelength = ... [tex] \sf{\lambda} [/tex]

Step by step :

[tex] \sf{c = c'} [/tex]

[tex] \sf{\lambda \times f = \lambda' \times f'} [/tex]

[tex] \sf{\cancel{\lambda} \times \cancel f = x \cancel{\lambda} \times 3 \cancel{f}} [/tex]

[tex] \sf{1 = 3x} [/tex]

[tex] \sf{x = \frac{1}{3}} [/tex] (Q.E.D)

Conclusion

So, if the frequency value is increased by a factor of 3 from its original, then the wavelength will decrease by a factor of 3 from the original.

See More

  • An example of calculating the frequency of an electromagnetic wave https://brainly.com/question/26437116
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