Unit 04 - Sound

Beat Frequency  When two sounds of slightly different frequencies are played together, the result is a sound with an alternating loud-soft pattern.  These alternating sound intensities are called beats and are the result of constructive and destructive interference.

Beat Frequency  The ear "hears" beats when the difference in the two frequencies is less than 7 Hz.  The ear determines the two frequencies or pitches to be the same, just out of tune.  When the frequencies are more than 7 Hz, the ear perceives this as two distinctly different sounds.  The faster the beats, the further apart the frequencies, the slower the beats, the closer the frequencies. No beats means the two frequencies are the same.

Applications  1. Piano tuners use beats to tune pianos. They pluck a piano string at the same time as sounding a tuning fork or an electronic tuner. If there are beats they slowly adjust the string to get fewer and fewer until no beats are heard. The string is now in tune.  2. Musicians are constantly listening and eliminating beats from their practicing or performing so they play "in tune".  3. Keyboards and other electronic instruments sometimes use effects created by beats for a tremelo or vibrato (vibrating) effect. The right amount of tremelo tends to give a warm and mellow sound

Beat Diagram  When C (compression) and R (rarefaction) from both frequencies line up, there is destructive interference, canceling out the sound.  When R from both frequencies line up, there is constructive interference resulting in a loud sound.  When moving from soft toward loud on the chart, notice that the C's and R's from both frequencies start to line up more and more until the two R's are perfectly in line. As the C's and R's get more in line with each other, the sound gets louder and louder - there is more constructive interference.  2 beats are heard in 1 second of time. Therefore we say that the beat frequency is 2 beats per second.

Beat Diagram  The following chart shows how beats are formed from constructive and destructive interference using 14 and 16 Hz sounds  f 1 and f 2 are slightly different frequencies (eg. 14 and 16 Hz).

Beat Calculations  Beat frequency can be solved mathematically by using the formula: where f 1 and f 2 are the frequencies of the two sources.

Example:  A tuning fork with a frequency of 440 Hz is sounded together with a note played on a piano. Eight beats are heard in 2 seconds. What is the frequency or pitch of the piano note? First find out how many beats are heard in 1 second. Beat frequency = 8 beats = 4 Hz 2 s Next use the beat frequency formula and solve:

Example:  There are 2 possible answers. There must be a difference of 4 Hz between the tuning fork and the piano note. Both f 2 answers give us that difference.  Without more information, you cannot arrive at just one answer.  Note: If the absolute value part of the equation above gave you some trouble, find the answer this way: Just add the beat frequency (4Hz) to 440 for one answer. Subtract 4 Hz from 440 to find the second answer.