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This is a fundamental question. I tried to find answers online but got confused. So, I'm asking here in hope of a simple and straightforward explanation.

Lets say we have a wave with amplitude x and frequency f. So, if I were to increase the frequency then I can reduce the wavelength which will cause increase in amplitude(because of compression of wave). Now, amplitude is increasing with increase in frequency but I have been told the opposite.

Am I getting something wrong?

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Amplitude and angular frequencies are independent of one another. Take a look at position of vibrating spring.

$$x=Acos(\omega t)$$ Where $A$ is amplitude and $\omega$ is frequency. If you pull and release the spring after some moment, it will keep moving up and down. So it across the same after some moment. And graph of position of the spring will look like sinusoidal and cosinusoidal. And the bigger the amplitude is the bigger the phase will be.

Generally, angular frequency doesn’t care what amplitude.

Click on play button of $A$ in Desmos

enter image description here

From the answer, you can see that energy is proportional to 'angular frequency and amplitude' squared. $$E\propto \omega^2 A^2$$

enter image description here

As you increase or decrease the angular frequency the energy changes.

enter image description here

But if you want the energy to be unchanged then energy will be constant. Let's assume that E=1 J, $$1\propto \omega^2 A^2$$ $$\implies \frac{1}{\omega}\propto A$$. To keep the energy unchanged, if you change frequency then you have to change amplitude also. Since they are inversely proportional then if one increases then another will decreases.

Thanks to Cort Ammon

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  • $\begingroup$ I'd add that, while mathematically speaking, frequency and amplitude are independent, in practical situations there is often a second equation that couples them. For example, in florescence, energy is conserved, and higher frequency waves of the same energy must have lower amplitude. This addresses what the OP is questioning when they were told that amplitude decreases with increased frequency. $\endgroup$
    – Cort Ammon
    Commented Feb 11, 2022 at 18:21
  • $\begingroup$ @CortAmmon It's new to me. I haven't heard anything like that. Even I searched equation which describes that but end up with nothing. Would you please elaborate? Or answer the question? $\endgroup$
    – Billy Istiak
    Commented Feb 12, 2022 at 6:31
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    $\begingroup$ Energy in a wave is proportional to the amplitude times the frequency, squared. So if you raise the frequency in a way that doesn't increase the energy, the amplitude must decrease. $\endgroup$
    – Cort Ammon
    Commented Feb 13, 2022 at 2:07
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if I were to increase the frequency then I can reduce the wavelength which will cause increase in amplitude(because of compression of wave)

This is not generally correct. The amplitude and the frequency of a wave are independent, and either can change without changing the other. To get the kind of relationship you are describing there must be some other constraint involved.

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