Yes.Sho Kano said:
Consider summing two tones of the same amplitude, A sin(ωt)+A sin(ψt). Do you know a way to write that as a product of trig functions?Sho Kano said:
##2A[sin(\frac{wt+ \varphi t}{2})cos(\frac{wt-\varphi t}{2})]## There's an average in the sine, but not in the cosine, how does this relate to an average freq?haruspex said:
Assuming ψ and ω are similar in value, that product has one frequency as the average of those and the other factor a much lower frequency. Mathematically that does not make them fundamentally different, but to a human observer it will sound and look like a wave of the average frequency with an amplitude varying at the much lower (beat) frequency.Sho Kano said:
Beat frequency is the difference in frequency between two sound waves that are slightly different in frequency. This difference in frequency creates a pulsing or beating sound.
Beat frequency is calculated by subtracting the lower frequency from the higher frequency. For example, if one sound wave has a frequency of 400 Hz and another has a frequency of 405 Hz, the beat frequency would be 5 Hz.
Beat frequency is caused by the interference of two sound waves with slightly different frequencies. When these waves overlap, they create areas of constructive and destructive interference, resulting in the pulsing or beating sound.
Beat frequency can be used to tune musical instruments by adjusting the frequency of one note until it creates a beat with the other note. It can also create interesting effects in music when used intentionally, such as in the use of tremolo or vibrato.
No, beat frequency is not harmful. It is a natural phenomenon that occurs in nature and is often used in music and sound engineering. However, prolonged exposure to loud sound waves, including those with beat frequency, can damage hearing. It is important to protect your ears from loud sounds and take breaks from exposure to loud noises.