The term “beat frequency” is associated with:
a) Resonance
b) Coupled oscillators
c) Forced vibration
d) Phase angle
The correct answer and explanation is:
The correct answer is b) Coupled oscillators.
Beat frequency occurs when two oscillators (usually sound waves or mechanical systems) of slightly different frequencies interact with each other. This phenomenon produces a variation in the amplitude of the resultant wave that oscillates at a frequency equal to the difference between the two original frequencies. It is particularly noticeable in sound, where two notes that are close in pitch can create a “pulsing” or “beating” sound. The beat frequency is defined as the absolute value of the difference between the frequencies of the two oscillating sources.
This phenomenon occurs because when two waves are in phase, their amplitudes combine, creating a louder sound. When they are out of phase, the amplitudes partially cancel each other out, creating a quieter sound. The result is a fluctuating intensity or volume, which is heard as a “beat” or periodic rise and fall in the sound level.
Beat frequency is commonly observed in various contexts. In music, when two instruments play nearly identical notes, the beating effect can be heard. It can also occur in mechanical systems where two oscillating objects have close but slightly different frequencies, such as in tuning forks or coupled pendulums.
The concept is tied to coupled oscillators, as these systems involve two or more oscillators that interact with one another. In coupled systems, the energy of one oscillator can transfer to another, and when the frequencies are close, the energy exchange manifests as a beat frequency. This is in contrast to other phenomena like resonance or forced vibration, which involve a system being driven at a single frequency or an external force acting on an object.
Beat frequencies are useful in various fields, including acoustics, musical tuning, and physics experiments dealing with wave interactions.