Hearing Beats in Music Musicians sometimes tune instruments by playing the same tone on two different instruments and listening for a phenomenon known as beats. Beats occur when two tones vary in frequency by only a few hertz. When the two instruments are in tune, the beats disappear. The ear hears beats because the pressure slowly rises and falls as a result of this slight variation in the frequency. ( Source: Pierce. J., The Science of Musical Sound. Scientific American Books.) (a) Consider the two tones with frequencies of 220 Hz and 223 Hz and pressures P 1 = 0.005 sin 440π t and A = 0.005 sin 446π t, respectively. A graph of the pressure P = P 1 + P 2 felt by an eardrum over the 1-sec interval [0.15. 1.15] is shown here. How many beats are there in 1 sec? (b) Repeat part (a) with frequencies of 220 and 216 Hz. (c) Determine a simple way to find the number of beats per second if the frequency of each tone is given.
Hearing Beats in Music Musicians sometimes tune instruments by playing the same tone on two different instruments and listening for a phenomenon known as beats. Beats occur when two tones vary in frequency by only a few hertz. When the two instruments are in tune, the beats disappear. The ear hears beats because the pressure slowly rises and falls as a result of this slight variation in the frequency. ( Source: Pierce. J., The Science of Musical Sound. Scientific American Books.) (a) Consider the two tones with frequencies of 220 Hz and 223 Hz and pressures P 1 = 0.005 sin 440π t and A = 0.005 sin 446π t, respectively. A graph of the pressure P = P 1 + P 2 felt by an eardrum over the 1-sec interval [0.15. 1.15] is shown here. How many beats are there in 1 sec? (b) Repeat part (a) with frequencies of 220 and 216 Hz. (c) Determine a simple way to find the number of beats per second if the frequency of each tone is given.
Solution Summary: The author explains how the number of beats in 1 sec can be calculated by graphing calculator Ti-83.
Hearing Beats in Music Musicians sometimes tune instruments by playing the same tone on two different instruments and listening for a phenomenon known as beats. Beats occur when two tones vary in frequency by only a few hertz. When the two instruments are in tune, the beats disappear. The ear hears beats because the pressure slowly rises and falls as a result of this slight variation in the frequency. (Source: Pierce. J., The Science of Musical Sound. Scientific American Books.)
(a) Consider the two tones with frequencies of 220 Hz and 223 Hz and pressures P1 = 0.005 sin 440πt and A = 0.005 sin 446πt, respectively. A graph of the pressure P = P1 + P2 felt by an eardrum over the 1-sec interval [0.15. 1.15] is shown here. How many beats are there in 1 sec?
(b) Repeat part (a) with frequencies of 220 and 216 Hz.
(c) Determine a simple way to find the number of beats per second if the frequency of each tone is given.
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