Are frequency and energy related?

[**Mariam**]

Hello, I am studying about waves and simple harmonic motion.
I have a confusion; when we studied the formula for period of pendulum and spring (T=2pi(rad(m/k))), it can be deduced that period doesn't depend on amplitude and so does frequency (T=1/f)
Then we learned about how amplitude and energy are proportional.

But then recently I was reading about electromagnetic waves and it said that "the energy transmitted by the waves is in direct proportion to their frequencies."

So how is frequency and energy related if frequency and amplitude are not??

 

[PietKuip]

The energy of the quanta of EM waves is proportional to frequency. Those quanta of energy are the photons.

For EM-waves, energy transmitted is proportional to the square of the amplitude of the fields.

 

[sophiecentaur]

So how is frequency and energy related if frequency and amplitude are not??

One way to think of it is that Amplitude (or at least Power transferred) corresponds to the number of photons arriving per second. High frequency EM has high energy photons (it comes in big dollops of energy) and low frequency EM comes in small dollops. So the same power of EM wave involves fewer photons at high frequency than the number at low frequency.
Your confusion is quite reasonable here because there is the Quantum issue to be considered, with EM. The Energy of a photon is very relevant when individual photons are interacting (say in a photographic process, photosynthesis or in photovoltaic cells) but, when something is just getting heated up by EM radiation, its the total power flux that counts. There is, in fact, no contradiction in the statements you are quoting.

 

[sophiecentaur]

In fact electromagnetic waves need not be sinusoidal at all.

Neither do any other waves - e.g. sound (Shouts loudly and very non-sinusoidally!)

 

[PietKuip]

Shm and electromagnetic waves are two different phenomenon. In case of shm you are absolutely correct in saying that it is directly proportional to amplitude. Electromagnetic waves are generated due to a moving charge or photon. The energy emitted by them is purely dependent upon frequency and is in no way related to shm. Plank experimentally found out this result which we today know as the Plank's equation. In fact electromagnetic waves need not be sinusoidal at all.

Zabini, this is wrong. Two obvious points:

• The energy of simple harmonic motion of a mass-spring system is proportional to the square of the amplitude
• Planck was a theorist