Question

wave y and wave z are two types of electromagnetic waves traveling through a vacuum. suppose the frequency of wave y is about three times greater than the frequency of wave z. which best compares the energy transferred by the two waves? it is the same for each wave because the amount of energy transferred is constant in all types of electromagnetic waves. wave y transfers about one - third the amount of energy as wave z because energy and frequency have an inverse relationship. wave y transfers about three times the amount of energy as wave z because energy and frequency have a direct relationship. it is zero for each wave because when waves travel through a vacuum, they do not transfer energy.

Explanation:

Step1: Energy - frequency relationship

The energy of an electromagnetic wave is given by the formula \(E = h
u\), where \(h\) is Planck's constant (\(h= 6.626\times10^{-34}\space J\cdot s\)) and \(
u\) is the frequency of the wave.

Step2: Comparing energies

Let the frequency of wave \(Z\) be \(
u_Z\). Then the frequency of wave \(Y\) is \(
u_Y = 3
u_Z\).
The energy of wave \(Z\), \(E_Z=h
u_Z\).
The energy of wave \(Y\), \(E_Y = h
u_Y=h(3
u_Z) = 3h
u_Z\).
So, \(E_Y = 3E_Z\). This shows that energy and frequency have a direct relationship (as frequency increases, energy increases proportionally).

The first option is wrong because the energy transferred by electromagnetic waves is not constant (it depends on frequency). The second option is wrong because energy and frequency are directly proportional (\(E\propto
u\), not inversely proportional). The fourth option is wrong because electromagnetic waves do transfer energy as they travel (for example, light - an electromagnetic wave - can heat objects, which is a form of energy transfer).

Answer:

Wave Y transfers about three times the amount of energy as wave Z because energy and frequency have a direct relationship.