Why the energy that waves transfer is only dependent on amplitude

[Karagoz]

Hi,

I wonder why the energy that waves transfer is only dependent on amplitude?

E.g. in this animation:
http://lifecdn.dailyburn.com/life/wp-content/uploads/2015/02/2.Alternating-Slam4.gif

The waves on the rope transfer energy to the items on the right side.

Wouldn't there be transferred more energy if the man produced faster waves, but with same amplitude?

Or waves transfer energy to the boat on water (by moving the boat up and down).

Even if the amplitude of the water waves was the same, with faster waves, the boat would move more up and down than if the waves were slower.

So wouldn't the waves transfer more energy to the boat if the speed of the waves was faster, even when the amplitude is same?

(btw, I'm very very new to physics).

 

[sanpokhrel]

Hey, i don't know if you know that or not, speed of the wave in a medium is constant for a given condition. So, for a given wave if frequency is constant then the wave transfer same energy for given amplitude. But if frequency increases then for the same time there will be more disturbance in the medium, so the energy transferred by that wave is more due to its frequency keeping the amplitude constant.

 

[sophiecentaur]

This link discusses exactly what you are asking about. Every cycle involves energy input so more cycles per second means more Power.

 

[Karagoz]

But what about frequency?

As higher the frequency, more will there be disturbance, hence more energy will be transferred?

Higher frequency in wave (not photons or light wave, but other waves) means more energy?

 

[CWatters]

I wonder why the energy that waves transfer is only dependent on amplitude?

Is it? See the link sophiecentaur posted. It contains this equation..

 

[CWatters]

Perhaps get a rope and try it out. Is it harder for you to shake the rope faster (eg at a higher frequency)?

 

[Karagoz]

Is angular frequency is something similar to frequency of the wave, which is measured with Hertz?

This is what's written in physics textbook for students (translation):
"We know how water waves transfer energy to a boat. They put the boat into swings with same frequency as waves' frequency. How much energy the boat gets, is not dependent on the wave-frequency , but dependent on amplitude. Bigger the amplitude the waves have, higher the boat will get lift up, and thus more energy it will get. All waves, including sound waves too, transfer energy that way." (in later paragraphs it explains that photons and light waves work differently).

This is why I get confused.

 

[sophiecentaur]

"We know how water waves transfer energy to a boat.

Water ('surface') waves have a different formula for energy, speed and wavelength and they are not the best waves to discuss for a starter. It's best to sort out waves on strings or normal sound waves before getting involved with surface waves on fluids, which don't follow the normal rules.

 

[CWatters]

Good catch.

 

[CWatters]

Is angular frequency is something similar to frequency of the wave, which is measured with Hertz?

Yes. ω = 2πF
https://en.wikipedia.org/wiki/Angular_frequency

 

[sanpokhrel]

But what about frequency?

As higher the frequency, more will there be disturbance, hence more energy will be transferred?

Higher frequency in wave (not photons or light wave, but other waves) means more energy?

Yes, it means higher energy as long as you keep amplitude constant for the wave.