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On this wave animation website, I noticed that on the section titled "From high to low speed (low density to high density)", there's an animation of a wave losing amplitude as it goes from a low density to high density region.

Why does the amplitude of the wave change because of the wave speed? I thought that wave speed/frequency/wavelength never changed amplitude, so this was really confusing to me.

enter image description here

I found another example of this here. I thought that increasing the volume of sound increases the amplitude of the sound, so I thought the answer was (A). However, the answer is (C), and somehow wave speed is also being changed by the volume.

These 2 examples make me think there's some relation between amplitude and wave speed, but I haven't found any resource/website that talks about a relationship between the two. Is there one?

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For the speaker example, the amplitude of the paper cone in the speaker must increase in order to increase the volume that the speaker emits. For a fixed frequency, assuming a pure tone (sinusoidal) output, this increase in amplitude is associated with the speaker cone moving back and forth in its housing. This movement must be accomplished in the same amount of time in which the lower amplitude movement occurred if the speaker is to maintain the same frequency. This means that the average velocity of the speaker cone must be higher at a higher volume because the cone must travel farther in the same amount of time.

The medium determines the wave speed. For the speaker, that speed is the speed of sound, which is approximately 330 m/s. Changing the volume of the speaker does not affect the speed of sound in air.

For the wave animation cited, as the wave goes from one density to another, part of the wave is reflected at the boundary. Since wave energy is a function of wave amplitude, conservation of energy requires that the amplitude of the transmitted wave must be smaller than it was before it was transmitted into the material of different density, because the reflected wave carries some of the energy of the incident wave.

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  • $\begingroup$ Thanks! At the end you say "because the reflected wave carries some of the energy of the incident wave". I was confused by that; I don't see where any reflection is taking place. $\endgroup$
    – APerson
    Commented Jan 5, 2019 at 14:03
  • $\begingroup$ @APerson, the video that I saw indicated a wave hitting the boundary from one string density to another. At the boundary, part of the wave was transmitted and part was reflected. This is standard when a wave of any sort goes abruptly from one medium to another, or encounters an abrupt transmitting medium density change. See the bottom two animations on your web link. $\endgroup$
    – David White
    Commented Jan 5, 2019 at 16:35
  • $\begingroup$ Oh, that makes a lot more sense. So, the energy (and thus the amplitude) of the wave decreases because part of the wave gets reflected backwards, correct? Why does a density change causes this reflection? $\endgroup$
    – APerson
    Commented Jan 7, 2019 at 23:40
  • $\begingroup$ @APerson, whenever a wave meets a boundary, part or all of the wave is reflected. An abrupt change in density is a boundary as far as the wave is concerned. $\endgroup$
    – David White
    Commented Jan 8, 2019 at 0:08

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