Beats in Sound Waves

The study of properties of sound in physics is known as acoustics. The term beats, is derived from this study. Beats in sound waves pertain to beat frequency. The common term, frequency, actually is the number of waves that pass through a fixed point in unit time. In reality, beats are the sound waves that reach our eardrums from two slightly similar frequencies, and we hear them like beats. Now, we will learn more about frequency and beat frequency and how this phenomenon of beats occurs.

Meaning of Frequency

Frequency means the number of waves that pass a fixed point in unit time. It can also be described as the number of vibrations or cycles a body undergoes during one unit of time in periodic motion.

• Frequency is a crucial parameter that is used in the fields of science and technology 

• It specifies the rate of oscillatory and vibratory phenomena 

• Similar phenomena that occur in nature are mechanical vibrations, audio signals (sound), light and radio waves 

• Usually, frequency is measured in the hertz unit. The Hertz measurement, abbreviated Hz, is the number of waves that pass by per second

What is a Beat Frequency?

Beats are a phenomenon in acoustics that alternate between loud and soft frequencies. It occurs when two waves of slightly similar frequency moving in the same direction meet at a point. We hear these two sound waves as alternating loud and soft vibrations in our eardrums, and we perceive it as a beating. 

As we talk about the beats phenomenon, we can calculate this:

• The beat frequency is the difference between the first wave and the second wave 

• The count of beats per second is equivalent to the difference of frequencies of the individual sound waves

fbeat = |f1 –  f2|, where the symbol | | means the absolute value.

To make it easier, let us consider two waves with two different frequencies, f1 = 16 hz and f2 = 17 hz, which are travelling in the same direction.

For example, imagine these waves – f1 and f2 – are travelling in one second (time). Let’s say the first wave has 10 oscillations, and the second one has 11. As the two waves start, these are in phase, meaning the peaks and valleys line up. The two waves add constructively at this point. This is not so if we look at these two waves with two different frequencies. After five oscillations, we see that the waves are definitely out of phase. When one is a maximum, and the other is a minimum, it is referred to as destructive interference. However, this incident will not last long. These waves are bound to come back into constructive interference as the two waves keep on travelling.

Two forks with somewhat similar frequency can be used in Physics’ practical or demonstration. The waves that each of these forks emit would depend on the length or the thickness of each fork. 

Constructive Interference

Constructive interference happens when two or more waves come together. It occurs when the waves are in phase with each other. In other words, the oscillations of these waves at a given point are in the same direction. Moreover, the resulting amplitude at that point is much larger than the amplitude of an individual wave. 

Destructive interference

Suppose two sound waves meet at a point. These waves will interfere so that the compression of one wave meets up with the rarefaction of a second wave, resulting in destructive interference. However, in general, whenever several waves come together, the interference will not be completely constructive or completely destructive, but somewhere in between.

Perception of beats

• If we consider our perception of beats, it is a complex phenomenon. If there are two notes: one note at 800 Hz and the other one at 807 Hz will beat at 7 Hz. Again, here it means that the sound will get louder and softer with a frequency of 7 Hz. Now, 7 Hz, or 7 oscillations per second, is a frequency you can keep up. If a clock is ticking at 7 Hz, you can count the individual ticks.

• We play two notes of 500 Hz and 650 Hz while another at 150 hz. Here, the sound will get louder and booming with a frequency of 150 Hz. Here, the frequency is too fast for our brain to process, so therefore these beats will not be interpreted by our brain as periodic change.

Recollecting facts

• The music that we hear is a mixture of sound waves. All music and songs have a collection of waves that have whole-number ratios regarding the frequencies that come with their notes.

• Destructive interference of sound waves becomes an important issue in the design of concert halls and auditoriums. The rooms must be designed in such a way as to reduce the amount of destructive interference. 

• The destructive interference of sound waves can also be used advantageously in noise reduction systems. Earphones have been produced that can be used by factory and construction workers to reduce the noise levels on their jobs.

• Another thing to remember is that the motions of waves of the particles or the waves transport energy and do not matter. This criterion makes them different from other phenomena in physics. 

Conclusion 

Waves travel from one point to another, and some can even travel through a vacuum. However, we had discussed sound waves with air as a medium which is the best example to understand. The phenomenon of beats in a medium of air is an important incident for any physicist. Waves that microwave your food, waves that carry messages even in space where there is no air, waves that are used for mobile technology, or waves that we listen to as music are all part of our human civilization. Understanding them is an important matter.