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Sorry if the question is stupid. The last time I touched physics was in school and I have never come back to it since. But this question popped up just recently in my life and I realized I don't know how to answer it.

As far as I remember, the amplitude of a sound wave defines the loudness of the sound - the bigger the amplitude is, the louder is the sound.

And I also remember that the frequency of a sound wave defines its pitch - the faster is the oscillation, the higher is the sound pitch.

Now imagine we take two oboes, each one playing the same note and with the same level of loudness. Both are producing a sound with the same amplitude. This means that the loudness of the resulting sound of two oboes will still be the same, but in the reality two oboes will sound louder than one. Why is it so?

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It is not always the case that the oboes will create louder sound. They may also create no sound! This is based on wave interference. When two waves, that have the same amplitude and frequency have their troughs and crests aligned, they can be added together (This is known as constructive interference) according to a principle known as superposition, and create a sound that is twice as loud. However, if the crests of one wave align with the trough of the other one, they will cancel (This is known as destructive interference) and there will be no sound. A visual representation is as follows enter image description here

If you would like more details about the topic, you can head to the Wikipedia page.

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    $\begingroup$ The reason two oboes do not cancel each other out is not just because the players (or instruments) do not generate the exact same sound, but it also depends on the distance between them. Their distance has to account for phase offset of $\pi$ (or $180^{o}$) in all frequencies for the waves to cancel out. This is impossible in practice and this is why they never cancel out. A "statistical" treatment of the two sounds would lead to an increase in their level of about $3 dB$ which corresponds to their energy being summed. As Belal Bahaa mentioned sound-cancelling headphones use this (cont.) $\endgroup$
    – ZaellixA
    Commented Aug 25, 2022 at 12:03
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    $\begingroup$ principle to reduce noise at the ear canal position, but you'll notice that this happens only for low and mid-low frequencies, due to their relatively large wavelengths. For higher frequencies even a small "error"/"discrepancy" in the position of the cancelling speaker or monitoring microphone can lead to considerable phase errors and thus, in the best case scenario, provide no cancellation, or even worse, increase the noise. $\endgroup$
    – ZaellixA
    Commented Aug 25, 2022 at 12:05
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    $\begingroup$ There is no instruments that have the exact same timbre. This is, the spectral content (frequency response) of each instrument is somewhat different, even when we talk about two oboes, cellos, violins, etc. Additionally, due to the fact that they are played by humans (not robots), means that there will be some timing differences between the performance of each instrumentalist. In order for two "sounds" to cancel each other out they must be identical, which is not the case with two real instruments plus, they must reach the position that they are supposed to cancel at the same time (cont.) $\endgroup$
    – ZaellixA
    Commented Sep 18, 2022 at 17:19
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    $\begingroup$ (conted.) Thus, even if the two instruments do produce the exact same sound (same frequency components and relative amplitudes) they should reach the listening position at the exact same time (this is practically impossible when they are played by humans), and even then, the cancellation would occur for only one specific point in space, because if you were to move from this point, the phase difference of the two sounds would change, resulting in a different cancellation pattern. $\endgroup$
    – ZaellixA
    Commented Sep 18, 2022 at 17:22
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    $\begingroup$ Regarding the cancelling headphones, the distance from the speaker driver to the ear canal is known (approximately at least), so if you find out what the incoming (external) sound is you can play back the same sound but with polarity reversal (roughly speaking) and the two will cancel at the ear canal. Those headphones do have a microphone (at least one) to monitor the external sound and emit the appropriate signal from the speaker driver to cancel it. Please note that this is a rough, brief explanation with a lot of information omitted. $\endgroup$
    – ZaellixA
    Commented Sep 18, 2022 at 17:28

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