Understanding the Beat Phenomenon: How Equal Amplitudes Create Harmonious Tones

[longestline1]

I am confused by this:

Two sinusoidal tones of equal amplitude and with frequencies of 439 and 443 Hz are sounded simultaneously.

Name and describe (qualitavitively and quantitatively) what you hear.
Why is it important that the two waves have equal amplitudes for this effect to occur

 

[atyy]

Probably:
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/beat.html
I think the two sinusoids only need to have roughly equal amplitudes.

Please note the difference between beats - where the frequencies have to be close to be perceptually obvious, and "missing fundamental" effect, where the frequencies must be harmonically spaced:
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/subton.html#c2

 

[astrokreng]

? I can explain the phenomenon of harmonious tones created by equal amplitudes in the following way:

When two sinusoidal tones with different frequencies are sounded simultaneously, they interfere with each other and create a new sound wave. This is known as the beat phenomenon. The frequency of the resulting wave is the difference between the frequencies of the two original waves. In this case, the resulting frequency would be 4 Hz (443 Hz - 439 Hz = 4 Hz).

Qualitatively, when the two waves have equal amplitudes, the resulting sound is perceived as a steady tone with a slight pulsating quality. This is because the two waves are in perfect phase with each other, meaning their peaks and troughs line up, creating a consistent sound. This is known as constructive interference.

Quantitatively, the amplitude of the resulting wave is equal to the difference in amplitude between the two original waves. So if the two original waves have equal amplitudes, the resulting wave will also have an equal amplitude, resulting in a balanced and harmonious sound.

It is important for the two waves to have equal amplitudes for this effect to occur because if one wave has a significantly larger amplitude than the other, it will dominate the resulting wave and the beat phenomenon will not be perceived. This is because the larger amplitude wave will have a greater influence on the resulting wave, causing it to deviate from the true frequency difference between the two original waves. Therefore, equal amplitudes are necessary for the two waves to have equal influence on the resulting wave and for the beat phenomenon to be heard.