Assume that wave A and B are examples of electromagnetic radiation and that the wavelength of B is twice that of A.

Question

Which of the following statements is true? 

 

1. Wave A is traveling at a greater speed than wave B through a vacuum

2. The wavelength of A is directly related to the photon energy associated with wave A

3. The photon energy associated with wave B is twice that of the photon energy associated with wave A

4. The frequency of wave A is larger than the frequency of wave B

5. All of the above are correct 

Answer 1

Hi Lara:

 

   The key points are:

 

-- that all electromagnetic (EM) waves travel at the same speed in a vacuum (that in a vacuum part is key, because they can travel slower in a medium like glass (or even air, though the effect in air is very small).

 

-- that the frequency (f) and wavelength (λ) of an EM wave are inversely related (specifically, f = c_n/λ,  where c_n represents the speed of light in whatever medium); and

 

-- that the energy (E) of a light wave is directly related to its frequency by E = hf.  Thus, E is inversely  related to wavelength, which is why answer 2 is false.

 

In addition to answer 2, answer 1 is false due to the first point above.

 

Answer 3 is false, because it would imply that E is directly related to λ (thus twice the wavelength gives twice the energy), which is not true because of the inverse relationship between E and λ stated above in the third point

 

Answer 5 is incorrect, because 1, 2, and 3 are all false.

 

That leaves answer 4.  According to the second point above, frequency and wavelength are inversely related.  Thus, the larger a wave's wavelength, the smaller its frequency.  Wave B has a wavelength twice as large as wave A.  Thus, wave B should have a smaller frequency.  Saying that the frequency of Wave B is smaller than the frequency of Wave A is equivalent to saying that the frequency of Wave A is larger than the frequency of Wave B.  Thus, Answer 4 is true.

 

Answer 2

Lara,

 

As a physicist, I assure you that Steven answered correctly on all 5 points.  The correct answer is indeed (4).  Reason:  B has twice the wavelength of A, therefore has half the frequency of A, and therefore the frequency of A is twice that of B, so it is larger than the frequency of B.  We can also conclude that a photon of A carries exactly twice as much energy as a photon of B.

Answer 3

 The above answers are correct, and I have deleted my first answer.