First, I will expand a bit on what Fabrice said.

consider two singers singing an A at 220Hz (to make the maths easy.) No real world singer or instrument produces a pure sine wave, so there will be harmonics at 440, 660, 880, 1100Hz etc. The harmonics will also, for different examples of a given type of instrument/singer, tend to have the same type of phase relationship.

So, if our two singers or instruments have the 220Hz exactly out of phase, the 440Hz will be perfectly in phase! Where low frequencies are missing, your brain tends to fill them in https://en.wikipedia.org/wiki/Missing_fundamental

Regarding the idea that singers may not be singing the same frequency: the human ear is extremely good at differentiating frequencies. The difference between one note and the next on a scale (one semitone) is a ratio of 2^(1/12) or about 1.059:1. The semitone is divided into 100 cents, and 10 cents is considered seriously out of tune. For a 100Hz note that's about 0.6Hz, so for a short note, you're not going to hear singers going in and out of phase with each other. For a longer note you probably will.

If you want to hear what two sine wave sources sound like, you need a low pass filter. The silencers on large diesel engines are quite effective low pass filters (this is not intentional, it's just easier to silence high frequencies than low frequencies.) If you hear two train engines running together you will hear the sound fade in and out (I've heard this sound more in the United States where trains are commonly pulled by multiple engines than in the UK.)

Also, low frequencies are less attenuated by distance than high frequencies. You can hear the same sound from a twin engined plane (preferably propellor) when it is flying high above you. Again, sound fades in and out as the engines go in and out of phase. Note that the engines are synchronized as closely as possible, because rapid beats between the engine frequencies are annoying to the passengers: http://aviation.stackexchange.com/questions/14263/what-is-propeller-engine-sync-and-how-does-it-work

One other point: for two sine wave sources in an enclosed space, even if the direct signal from the sources is perfectly out of phase, the sound reflected off the walls will probably have a different phase relationship. So you will be able to hear the sound, it will just sound as if it is coming from somewhere else.

First, I will expand a bit on what Fabrice said.

consider two singers singing an A at 220Hz (to make the maths easy.) No real world singer or instrument produces a pure sine wave, so there will be harmonics at 440, 660, 880, 1100Hz etc. The harmonics will also, for different examples of a given type of instrument/singer, tend to have the same type of phase relationship.

So, if our two singers or instruments have the 220Hz exactly out of phase, the 440Hz will be perfectly in phase! Where low frequencies are missing, your brain tends to fill them in https://en.wikipedia.org/wiki/Missing_fundamental

Regarding the idea that singers may not be singing the same frequency: the human ear is extremely good at differentiating frequencies. The difference between one note and the next on a scale (one semitone) is a ratio of 2^(1/12) or about 1.059:1. The semitone is divided into 100 cents, and 10 cents is considered seriously out of tune. For a 100Hz note that's about 0.6Hz, so for a short note, you're not going to hear singers going in and out of phase with each other. For a longer note you probably will.

If you want to hear what two sine wave sources sound like, you need a low pass filter. The silencers on large diesel engines are quite effective low pass filters (this is not intentional, it's just easier to silence high frequencies than low frequencies.) If you hear two train engines running together you will hear the sound fade in and out (I've heard this sound more in the United States where trains are commonly pulled by multiple engines than in the UK.)

Also, low frequencies are less attenuated by distance than high frequencies. You can hear the same sound from a twin engined plane (preferably propellor) when it is flying high above you. Again, sound fades in and out as the engines go in and out of phase. Note that the engines are synchronized as closely as possible, because rapid beats between the engine frequencies are annoying to the passengers: https://aviation.stackexchange.com/questions/14263/what-is-propeller-engine-sync-and-how-does-it-work

One other point: for two sine wave sources in an enclosed space, even if the direct signal from the sources is perfectly out of phase, the sound reflected off the walls will probably have a different phase relationship. So you will be able to hear the sound, it will just sound as if it is coming from somewhere else.

First, I will expand a bit on what Fabrice said.

consider two singers singing an A at 220Hz (to make the maths easy.) No real world singer or instrument produces a pure sine wave, so there will be harmonics at 440, 660, 880, 1100Hz etc. The harmonics will also, for different examples of a given type of instrument/singer, tend to have the same type of phase relationship.

So, if our two singers or instruments have the 220Hz exactly out of phase, the 440Hz will be perfectly in phase! Where low frequencies are missing, your brain tends to fill them in https://en.wikipedia.org/wiki/Missing_fundamental

Regarding the idea that singers may not be singing the same frequency: the human ear is extremely good at differentiating frequencies. The difference between one note and the next on a scale (one semitone) is a ratio of 2^(1/12) or about 1.059:1. The semitone is divided into 100 cents, and 10 cents is considered seriously out of tune. For a 100Hz note that's about 0.6Hz, so for a short note, you're not going to hear singers going in and out of phase with each other. For a longer note you probably will.

If you want to hear what two sine wave sources sound like, you need a low pass filter. The silencers on large diesel engines are quite effective low pass filters (this is not intentional, it's just easier to silence high frequencies than low frequencies.) If you hear two train engines running together you will hear the sound fade in and out (I've heard this sound more in the United States where trains are commonly pulled by multiple engines than in the UK.)

Also, low frequencies are less attenuated by distance than high frequencies. You can hear the same sound from a twin engined plane (preferably propellor) when it is flying high above you. Again, sound fades in and out as the engines go in and out of phase. Note that the engines are synchronized as closely as possible, because rapid beats between the engine frequencies are annoying to the passengers: http://aviation.stackexchange.com/questions/14263/what-is-propeller-engine-sync-and-how-does-it-work

First, I will expand a bit on what Fabrice said.

consider two singers singing an A at 220Hz (to make the maths easy.) No real world singer or instrument produces a pure sine wave, so there will be harmonics at 440, 660, 880, 1100Hz etc. The harmonics will also, for different examples of a given type of instrument/singer, tend to have the same type of phase relationship.

So, if our two singers or instruments have the 220Hz exactly out of phase, the 440Hz will be perfectly in phase! Where low frequencies are missing, your brain tends to fill them in https://en.wikipedia.org/wiki/Missing_fundamental

Regarding the idea that singers may not be singing the same frequency: the human ear is extremely good at differentiating frequencies. The difference between one note and the next on a scale (one semitone) is a ratio of 2^(1/12) or about 1.059:1. The semitone is divided into 100 cents, and 10 cents is considered seriously out of tune. For a 100Hz note that's about 0.6Hz, so for a short note, you're not going to hear singers going in and out of phase with each other. For a longer note you probably will.

If you want to hear what two sine wave sources sound like, you need a low pass filter. The silencers on large diesel engines are quite effective low pass filters (this is not intentional, it's just easier to silence high frequencies than low frequencies.) If you hear two train engines running together you will hear the sound fade in and out (I've heard this sound more in the United States where trains are commonly pulled by multiple engines than in the UK.)

Also, low frequencies are less attenuated by distance than high frequencies. You can hear the same sound from a twin engined plane (preferably propellor) when it is flying high above you. Again, sound fades in and out as the engines go in and out of phase. Note that the engines are synchronized as closely as possible, because rapid beats between the engine frequencies are annoying to the passengers: http://aviation.stackexchange.com/questions/14263/what-is-propeller-engine-sync-and-how-does-it-work

One other point: for two sine wave sources in an enclosed space, even if the direct signal from the sources is perfectly out of phase, the sound reflected off the walls will probably have a different phase relationship. So you will be able to hear the sound, it will just sound as if it is coming from somewhere else.