A violinist and a pianist simultaneously sound notes with frequencies of 436Hz and 440 hz,respectively. What beat frequency will the musicians hear?
The musicians will hear a beat frequency of
The idea here is that two sound waves of different frequencies will interfere with each other and create variations in the intensity of the sound we hear.
More specifically, these variations correspond to regions where the sound waves undergo constructive interference, characterized by high volume sound, and regions where they undergo destructive interference, characterized by low volume sound.
This succession of loud sounds and soft sounds is what produces beat patterns.
The beat frequency tells you how many complete "beats" you get per second. The beat frequency is equal to the absolute value of the difference between the frequencies of the two sound waves.
#f_"beat" = |f_1 - f_2|#
In your case, the frequencies of the two sound waves are
#f_1 = "436 Hz" " "#and #" "f_2 = "440 Hz"#
which means that the beat frequency the two musicians will hear is
#f_"beat" = |436 - 440| = color(green)("4 Hz")#