Beat Frequency Formula

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What is Beat Frequency?

According to acoustics, a beat is an interference pattern between two sound waves of different sound frequencies or a periodical variation in volume. Here, both the waves should travel in the same direction.  The beat frequency is common in the tunning instruments, this will produce sustained beats, tones and they can readily be recognized. While tuning two tones to a unison will shows a peculiar effect. When the two sound waves, which are not identical are close in pitch will generate the beating. The volume of beats is varied like a tremolo as the sounds interfere are constructive and destructive.  When the tones gradually reach unison, the beats get slow down. If the two tones are separated, their beat frequency will approach the human pitch range perception. 

Beats are produced when the two waves of nearby frequencies are superimposed together. This will occurs when the two waves are travel in the same path. Beats also cause a periodic variation in the intensity of resultant waves.  The beat frequency is the no of beats formula produced per second. 

Beat Formula: fb =|f2−f1| 

f1 and f2 are the frequencies of the two waves. 

The value of beat frequency cannot be negative. 

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The above image shows the diagram of the beat frequency, constructive interference of beat frequency and destructive interference in beat frequency. 

Beat Frequency in Real Time 

Musicians will commonly use beats interference to check tuning at the perfect fifth, unison, or other simple harmonic intervals. Piano and organ tuners are also using this method to count beats, which are aiming to produce a particular number of specific intervals. 

Problems Based on Beat Frequency

Problem 1: Calculate the Beat Frequency if the Two Frequencies of Waves are 720Hz and 280 Hz Respectively?


From the given data, lets consider the values of f1 and f2 as given below/ 

f2 = 700Hz and f1 = 300Hz

The formula for beat frequency 

fb = |f2−f1|

fb = |700−300|= 400Hz

Therefore, the beat frequency of the above given two waves is 400Hz. 

Problem 2: Derive the Beat Frequency of the Wave, with Frequencies are 650 Hz and 800 Hz Respectively?


From the given data lets consider the values of f1 and f2 as given below. 

f1 = 650Hz and f2 = 800Hz

The beat frequency derivation (fb) 

 fb =|f2−f1|

fb= |800−650|= 150Hz

Therefore, the beat frequency of the above given two waves is 150Hz. 

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FAQs (Frequently Asked Questions)

Q1. Define Beat Frequency?

Ans: The beat frequency derivation shows the difference of frequencies between two waves. The beat frequency has both constructive and destructive interference. While hearing sounds, we can hear beat frequency as the rate at which the loudness of variation in sounds. In the same way, we can hear the ordinary frequency of the waves as the pitch of sounds. The values of beat frequency must be an absolute value, which shows the difference between the two frequencies. But the negative value in beat frequency is not possible. 

Q2. What Causes a Beat Frequency?

Ans: Beats can cause the interference of two waves at the same point in the same place. The plot of the discrepancy of resultant amplitude with time will show a periodic decrease and increase to form two sine waves. 

Q3. Can We Hear Beat Frequency?

Ans: If the beat frequency between the two waves is less than 10Hz,  then the waves are very close in frequency and we can hear the sound as one pinch. Here, the pinch denotes the average of frequencies of two waves.  Likewise, the loudness of the beat frequency completely depends on the frequency range. The beat frequency between the two waves can range from 10Hz to 60Hz.