Physics · Ch 6 — Superposition of Waves
Applications of beats
Applications of beats
The beats phenomenon has several genuinely practical applications. FIRST, musicians use beats to TUNE instruments to each other, or to a reference pitch: two notes are sounded together and adjusted (e.g. by tightening or loosening a string) until the beats slow down and eventually vanish entirely -- at that point the two frequencies are EXACTLY equal (in unison), and the instruments are correctly tuned, producing a pleasant combined sound rather than one degraded by audible beating. SECOND, an UNKNOWN sound frequency can be measured by beating it against a source of adjustable, precisely KNOWN frequency: the known source is tuned until the beat frequency between the two drops to zero, at which point the known source's (now-read-off) frequency exactly equals the unknown one.
THIRD, beats are also the underlying mechanism behind measuring the speed of a moving object using Doppler RADAR or SONAR, familiar already from the Doppler effect studied in Class XI: a source (radar gun, or a sonar transmitter for tracking submarines) sends out a signal of known frequency towards the moving object; the object reflects this signal back, but -- because the object and source are in relative motion -- the reflected signal's frequency is shifted from the original by the Doppler effect (applied, in effect, twice: once for the object 'receiving' the moving signal, and once again for the source receiving the signal reflected off the moving object). Comparing (i.e. beating) this Doppler-shifted, reflected frequency against the original transmitted frequency gives a measurable beat frequency, from which the object's speed can be calculated -- this is exactly how traffic …
Worked out. A hands-on activity, not a solved numerical: two tuning forks of the SAME nominal frequency are first vibrated and held side by side, with the student listening for the periodic rise and fall of loudness (beats) -- ideally none should be heard if the forks are truly identical, but small manufacturing/wear differences usually produce a slow, faint beat that the student is asked to count over one minute. A small blob of wax is then stuck onto the prongs of ONE fork (which lowers that fork's frequency slightly, since adding mass reduces a vibrating system's natural frequency) and the pair is sounded again, with the student asked to judge (from how the beat rate itself CHANGES after adding the wax) whether the waxed fork's frequency has increased or decreased relative to the other, and to use that reasoning to determine the new …