Beats

What do you understand by the term ‘beats’? Most of us might hold an image of a stereo or an amplifier throwing out heavy thumping. However, when it comes to physics everything has a perfect explanation! Therefore, let us try to get a better idea about ‘beats’ as a concept.

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Introduction to Beats

When two different objects vibrate at different frequencies, there is a fluctuating sound, this sensation is known as beats. In other words, when two sound waves having slightly different frequencies reach your ear, then you are able to hear fluctuating sound (alternate soft and loud sound). It is important to note that, the loud sensation of sound is produced by the constructive interference. On the other hand, the soft sound is instigated due to destructive interference.

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Constructive Interference

An interference is called constructive if two waves holding the same frequency reach a point in a way that the first wave crest meets the crest of the other wave. Considering a sound wave, when this happens then the amplitude of sound waves gets added. Hence, the resultant sound is quite louder as compared to the original sound.

Destructive Interference

This form of interference is termed as destructive when two waves holding the same frequency encounter in a manner where the crest of a particular wave meets the trough of the other. In the case of two sound waves, this phenomenon causes the amplitude of the specific sound waves to get subtracted. Hence, the resultant sound appears to be much weaker as compared to the original sound.

Beats Frequency

When two sound waves having different frequencies encounter each other, then the amplitude of sound waves is added & subtracted alternatively through a given period. Hence, the subsequent sound intensity swings (grows louder and softer) through the given period.

Let us consider two different sound waves, A and B of varying frequencies but having a similar amplitude propagating in the same medium. When these two sound waves encounter, a fluctuating sound can be heard. Do note that, for a certain time, the crest of A meets the crest of B. Hence, this causes constructive interference. Therefore, the sound intensity rises for this certain period. However, after a point of time, the crest of B meets the trough of A. In this scenario, destructive interference is experienced; this causes the intensity of sound to fall for a certain period.

Observations

• The intensity of sound increases and decreases continuously with time.
• Dissimilar to the original sound wave, the resultant sound wave has an amplitude which isn’t constant; it differs with respect to time.
• Also, whenever the sound intensity rises to maximum, it is called as waxing of sound. Conversely, when the sound intensity falls to a minimum, it is termed as the waning of sound.
• Overall phenomenon of periodic waxing & waning of sound, where two sound waves holding almost equal frequencies encounter each other is called beats.

Beat Frequency can be called as the number of beats generated per second, which is equivalent to the variance in frequencies of two sound waves. This has been converted into an equation for gaining a better understanding.

f_b = |f₁ – f₂|

Where,

• f₁ = sound wave 1 frequency
• f₂ = sound wave 2 frequency
• |f₁ – f₂| = Difference (positive value)
• f_b = beats frequency

Question For You

Q. Evaluate the beat frequency when two wave frequencies are 750Hz and 390Hz respectively?

Ans: Given details include, f₁ = 750 Hz and f₂ = 390 Hz

Therefore, the beat frequency can be calculated to be,

f_b = |f₁ – f₂|

f_b = |390−750|= 380Hz