Beat Frequency Formula

Beat Frequency Formula

Beat is a word that describes a wave of sound. The Beat Frequency Formula is the frequency difference between the two waves, and this is due to constructive and destructive interference. In sound, the beat frequency is heard as the rate at which the loudness of the sound changes, while the normal frequency of the wave is heard as the pitch of the sound. Here, students elaborate on the concept of beat frequency and the formula for beat frequency. How frequent strokes can be? When two of her waves of approximately the same frequency travel in the medium along the same direction and meet at a point, a beat is produced. When two sound waves of different frequencies approach the ear, they alternate between productive and harmful interference, so the sound alternates louder and quieter and this phenomenon is known as beating. Students can go to the Extramarks website for more information about the Beat Frequency Formula.

Beat Frequency Formula:

The Beat Frequency Formula is equal to the sum of the frequency changes of the two waves. The number of beats per second corresponds to the frequency difference between the two waves, called the Beat Frequency Formula.

Everyone loves to listen to the piano and tune for melodies. When someone plays the piano, the sound they hear when they hit the black and white keys on the keyboard is the interference of two sound waves. These superimposed waves (with slight variations in frequency) alternate between loudness and smoothness. This fluctuation is the beat. How does someone determine the frequency and phase difference of beats when they can’t see the waves? In this article, students can get the best explanation of this concept that will stay in their memory forever. What is meant by a beat in physics? Suppose someone’s friends invite him to their concert, and he hears the soothing sound of tuning forks coming through the speakers. If he likes science, he might be wondering what a beet is and what it looks like. The sound coming out of speaker S1 looks like this: What happens here is that the sound coming out of it collides with air molecules.  When a sound hits A1, it vibrates around the middle position. Now let’s draw a graph showing how the displacement of the air changes over time. If someone places another speaker S2 above S1, the graph thus formed looks like this: When these two waves overlap or interfere, you can see the difference in frequency in the graph below. If someone hears one loud tone, and they do not overlap, one hears a soft tone. So this change in volume and softness is a beat. Similarly, when more sound waves hit air molecules, one hears a whine. Tip: Beat formations must move in the same direction and be in the same phase. What is meant by the Beat Frequency Formula? From figure m students can see that the frequency of the pink wave is f1 and the frequency of the green wave is f2. The Beat Frequency Formula is therefore the difference between these two.

  • Important Note: The reason for preserving the sign of the modulus is that f1 can be less than f2, resulting in a negative value, which can become positive after exceeding the sign of the modulus. In a medium of equal amplitude but a slightly different frequency, it is supposed that two waves travel in the same direction, reach a certain point and interfere. The resulting sound intensity is called “increase” at the loudest and “decrease” at the smallest. A simultaneous increase and decrease is defined as a beat.

Derivation Of Beat Frequency Formula:

Imagine that sounds from two different sources whose medium is air meet at a point p. Suppose the period of the source is shorter than TS and the frequency is higher than f2, and the other sources have periods and frequencies of TL and f1. Students will use these frequencies to represent the Beat Frequency Formula by showing the relationship between these two frequencies.

As in our conceptual discussion, let’s start from the moment when the peak from each source is at point p. If the next peak from a shorter period source arrives after period TS has elapsed, the corresponding peak from the longer period source does not arrive for period DeltaT = TL – TS. In fact, as each successive short-period peak arrives, the corresponding long-period peak is further delayed by ΔT. Eventually, after a certain number of n short periods, the long period peak arrives at TL the full long period after the arrival of the corresponding short period peak.

n×ΔT=TL- (1)

This means that when a short-period peak arrives, a long-period peak precedes the corresponding long-period peak. This leads to constructive interference (loud noise). The beat period is the time it takes from when the interference is maximally constructive to when the interference is maximally constructive. Extramarks provides the best resources and solutions for every formula.

Solved Examples For Beat Frequency Formula

  1. Calculate the Beat Frequency Formula for two wave frequencies of 750 Hz and 380 Hz respectively.


The given parameters are

f2=800Hz, f1=400Hz

The Beat Frequency Formula  is given by:

fb = |f2−f1|

fb = |800−400|= 400Hz

2. Calculate the Beat Frequency Formula for wave frequencies of 550 Hz and 1000 Hz respectively.


The known number is

f1 = 550Hz and f2 = 1000 Hz

The Beat Frequency Formula is thus expressed as:

fb =|f2−f1|

fb= |1000−550|= 450Hz

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