Hello students we have learnt that when two sound waves overlaps, i.e interference of sound is takes place the intensity of sound is appeared to change. During constructive interference i.e. when sound waves overlaps in a phase (with path difference of integral multiple of nλ), the resultant intensity increases, whereas during constructive interference two waves overlaps out of phase (with path difference of odd multiple of λ⁄2), the resultant intensity of sound decreases.
This alternate change in intensity of sound forms the beats.
Let’s define some important concept from the article……………!
Formation of beats
The production of alternate waxing and waning sound due the superposition of two sound waves of equal amplitude but slightly different frequencies is called beats.
Some important definitions:
- Waxing: The Maximum of sound is called waxing. (i.e. resultant amplitude should be maximum)
- Waning: The minimum of sound is called waning. (i.e. resultant amplitude should be minimum)
- One beat: The waxing & one waning is forms one beat.
- Period of beat: The time interval between two successive waxing (and waning) is called the period of beat.
- Beat frequency: The number of beats heard per second is called beat frequency.
Let’s illustrate the concept in more detail……………!
Consider the two eaves producing beats.et ‘a’ be the amplitude and n1,n2 be the frequencies of the two waves such that n1 > n2.
The displacement of particle,
Y1 = a sinω1t = sin2πn1t ……….(1)
Y2 = a sinω2t = sin2πn2t ……….(2)
∴ The resultant displacement is given by the principle of superposition of waves.
∴Y = Y1 + Y2
Y = a sin2πn1t + a sin 2 πn2t
Equation (3) shows that resultant motion is also simple harmonic motion, where ‘R’ is amplitude of resultant motion.
- Conditions of waxing: For waxing the amplitude should be maximum so that,
The period of waxing is the time between alternating waxing.
∴T = 1/n1-n2
Therefore the frequency of waxing is given as,
N = n1 – n2………(4)
- Conditions of waning:- For waxing the amplitude should be minimum so that,
R = 0
The period of waning is the time between alternating waning.
T = 1 / n1 – n2
Therefore the frequency of waning is given as,
N = n1 – n2
From equation (4) and (5) we conclude that the waxing and waning are alternately situated in a medium, when waves interferes each other.
Let’s discuss some important applications of beats:
- To determine the unknown frequency of tuning fork.
- To tune the musical instrument.
- To detect the poisonous gas present the mines.
- RADAR: Used in defence system
- The Doppler Effect in an ultrasonic setup detects the reflected sound from moving blood.