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I don't think there is any relationship in frequency and loudness, and frequency only affects the pitch of the wave. But could a really high frequency somehow affect the amplitude of a transverse wave in real-life conditions?

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    $\begingroup$ Please be more specific. The intensity of a sound can be measured by instrumentation. The loudness of a sound is what humans interpret as sound intensity, and that interpretation does indeed depend on frequency, whereby sound must be very intense on the low end (e.g., 20 Hz) and high end (e.g., 20,000 Hz) of the "human range" in order to be heard. $\endgroup$ Oct 30, 2019 at 21:14
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    $\begingroup$ One also has to watch out for implicit assumptions. If you ask "How does chaning the frequency affect the loundness?" when you mean "How does spinning the frequency dial on this sound source affect loundness?" the answers you get may be based on incorrect assumptions. $\endgroup$ Oct 30, 2019 at 21:18

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I first want to clarify a few terms as they are commonly used in acoustics:

  • Frequency is the number of times per second that the sound pressure changes from low to high.

  • Amplitude is an objective physical measure of the strength of the sound wave. For a sound wave with an amplitude of 1 Pa, the high sound pressure is the atmospheric pressure plus 1 Pa, while the low sound pressure is atmospheric pressure minus 1 Pa. Put simply, sound amplitude is often expressed logarithmically as decibels.

  • Loudness is the subjective perception of how strong the sound is. This perception depends on individuals' hearing. For example, someone with age-related hearing loss would typically percieve a high-frequency sound as less loud than someone with "normal" hearing.

People's hearing is also more sensitive to some frequencies than others. In other words, if you play sounds at different frequencies but the same amplitudes to a person, he or she would perceive them as having different loudness. This effect is often characterised through equal-loudness curves such as the ones below.

enter image description here

Sounds along each of the red lines are, on average for humans, perceived as equally loud. This shows us that people are much less sensitive to low-frequency sound, and most sensitive around 3–4 kHz, although this effect diminishes as sounds get louder. This is a well-understood effect that is taken into account when setting limits for or measuring noise from e.g. traffic or industry.

I hope that answered your question!

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I believe that Erlend gave a quite instructive answer, so I will try to stand only on one point of your question. You kinda mix loudness, amplitude and frequency in a more objective way than a subjective one (as would the inclusion of loudness in the conversation would demand), and you seem to be interested to know if the frequency of a wave would affect (somehow) its amplitude.

First of all, frequency is the repetition rate of a "phenomenon" and shows how often something is happening. It is not very clear what "a frequency could affect the amplitude" means, so I will assume that you are asking whether at very high frequencies the wave behaves differently.

In the most fundamental treatment of waves we assume that the media in which sound "travels" are linear in nature. This is of course not always the case, definitely not the case in real life and sometimes even a not so good approximation. Now, in these simple cases (in an ideal massless string for example) the amplitude of the frequency components depend on the properties of the medium, the boundary and initial conditions. Apart from that we assume that otherwise the medium treats the waves with different frequencies in a consistent way.

Of course in real life this in not the case and attenuation as well as propagation in media are frequency dependent (dispersive media in the propagation case). For example, most often than not, high frequencies are attenuated faster than low frequencies.

That being said, if you don't take into account the non-linearities then the answer is no. On the other hand, since you ask about real-life, non-linearities play a role here. Unless one considers a resonant phenomenon though, you can't really have extreme amplitudes on specific frequencies. Even when it comes to resonances, many real life vibrating systems exhibit high damping or even low coupling to the surrounding medium to produce so high amplitudes in a very narrow bandiwdth.

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The low frequency can be lower than high frequency if the number of watts per hertz is constant.

A wave can be having many smaller waves like a box with several small boxes inside them and we are having two values for the number of waves

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