# If two waves on a string have the same amplitude but different frequencies, does the wave with greater frequency also have more energy?

I'm trying to better understand the dependency of mechanical wave energy on amplitude and frequency. From what I understand, mechanical wave energy depends on both but many of the examples that I have read about focus on amplitude and not frequency.

• Commented Feb 20, 2017 at 17:11
• Yes. That is one of the reasons why I asked my question. The formula offered by the site clearly shows that mechanical wave energy depends on frequency. Yet, so many examples, especially those geared toward introductory physics students, focus solely on amplitude. I think authors should focus more on the fact that shaking a rope faster in addition to shaking it over a greater distance from equilibrium invests more energy into the medium Commented Feb 20, 2017 at 17:20
• Then you should ask rather - why some authors omit the frequency in the total energy formula? It would be no easy answer. Oh, possibly - they want to make it more clear/easy to learners? Commented Feb 20, 2017 at 17:23

Sound in air would be a good analogy for your question because we can have both frequency and amplitude in the air. There are 2 variables here, the size of the pulse (volume) and the frequency (pitch). Any combination is possible at any energy level. (The speed of sound is fixed in the air at constant conditions.)

In many environments it is easier to control amplitude, like water wave experiments. So it is more common to talk about waves and amplitude. Another variable is the duration of the wave/signal ... more energy is in a sound that lasts a longer time.