Beats in Sound Waves

Summary

The script explores the phenomenon of 'beats' in acoustics, where two sound waves of nearly equal frequencies and amplitudes create a fluctuating sound intensity. It explains how beats occur when two waves superimpose, resulting in a rhythmic pattern of sound intensity maxima and minima, with the beat frequency being the difference between the two original frequencies. The importance of nearly equal frequencies for distinct beats is highlighted, as well as the persistence of hearing, which requires the time interval between beats to exceed one-tenth of a second for them to be perceptible. A graphical method using two tuning forks illustrates the formation of beats.

Takeaways

• 😀 Beats occur when two sound waves of nearly equal frequencies and amplitudes superimpose.
• 🔊 The intensity of the resultant sound alternates between high and low as the waves interact.
• ⏲️ A beat is formed when the sound intensity reaches a maximum, then minimum, and maximum again over time.
• 🎶 The time interval between two successive beats is called the beat frequency.
• 🎼 For example, when sounds of 256 Hz and 260 Hz are combined, they produce a beat frequency of 4 Hz.
• 🔄 The frequency of the beats is the difference between the frequencies of the two combining sounds.
• 🔍 For distinct beats to be heard, the frequencies of the two sources must be nearly equal, typically with a difference of less than 10 Hz.
• 👂 The persistence of hearing causes the impression of sound to last about one-tenth of a second, affecting how beats are perceived.
• 📉 In graphical terms, compressions and rarefactions of the sound waves from two sources can be visualized to understand beat formation.
• 🔄 When compressions of one wave coincide with compressions of another, the resultant intensity is maximum; when they do not align, the intensity is minimum.

Q & A

What is the phenomenon called when two sound waves of nearly equal frequencies superimpose on each other?

The phenomenon is called 'beats.' It occurs when two sound waves of nearly equal frequencies and amplitudes traveling in the same direction superimpose, causing the intensity of the resultant sound to alternate between maximum and minimum.

What is meant by the 'intensity of sound' in the context of beats?

The 'intensity of sound' refers to the loudness or strength of the sound wave, which in the case of beats, varies with time due to the superposition of two nearly equal frequency sound waves.

How is the beat frequency related to the frequencies of the two sound waves involved?

The beat frequency is the number of times the intensity of the sound goes from maximum to minimum and back to maximum in one second. It is equal to the difference in frequencies of the two sound waves that are superimposing.

Why should the frequencies of the two sound sources be nearly equal for distinct beats to be heard?

For distinct beats to be heard, the frequencies of the two sound sources should be nearly equal because the difference in their frequencies must be small (less than ten). This ensures that the time interval between two successive beats is greater than one-tenth of a second, allowing our ears to distinguish between the beats.

What is the average frequency of the sound heard when two sound waves of 256 Hz and 260 Hz superimpose?

The average frequency of the sound heard when two sound waves of 256 Hz and 260 Hz superimpose is 258 Hz, which is the mean of the two combining frequencies.

What property of hearing is relevant to the perception of beats?

The property of 'persistence of hearing' is relevant to the perception of beats. It refers to the duration for which the impression of a sound persists in our mind, which is about one-tenth of a second, allowing us to mix up the impressions of two closely timed sounds.

What is the graphical method used to represent the formation of beats?

The graphical method involves representing the waves of compression and rarefaction from two sound sources as curves. By superimposing these curves according to the principle of superposition, one can visualize the resultant wave and the formation of beats.

How many vibrations does fork A complete in 1/4 of a second if its frequency is 4 Hz?

Fork A, with a frequency of 4 Hz, completes 1 vibration in 1/4 of a second (since 1 Hz = 1 vibration per second, 4 Hz = 4 vibrations per second).

How many vibrations does fork B complete in 1/2 of a second if its frequency is 8 Hz?

Fork B, with a frequency of 8 Hz, completes 4 vibrations in 1/2 of a second (since 8 Hz = 8 vibrations per second, half of that is 4 vibrations).

What happens to the resultant amplitude and intensity of sound when compression from one wave falls on compression from another wave?

When compression from one wave falls on compression from another wave, the resultant amplitude becomes maximum, and hence the intensity of the sound is also maximum.

What happens to the resultant amplitude and intensity of sound when rarefaction from one wave falls on compression from another wave?

When rarefaction from one wave falls on compression from another wave, the resultant amplitude becomes minimum, and hence the intensity of the sound is also minimum.

Outlines

00:00

🎵 Understanding Beats in Sound Waves

This paragraph explains the phenomenon of beats in acoustics, which occurs when two sound waves with nearly the same frequency and equal amplitudes superimpose on each other. The resultant sound's intensity varies with time, creating a rhythmic pattern. The beat frequency is the rate at which the intensity reaches its maximum and minimum, which is the difference between the two original frequencies. For distinct beats to be heard, the frequencies of the two sound sources should be nearly equal, with a difference of less than ten Hertz, allowing the human ear to distinguish between the two sounds. The example given is of two sound frequencies, 256 Hz and 260 Hz, which produce a beat frequency of 4 Hz, heard as a fluctuating sound intensity. A graphical method is also introduced to visualize the superposition of two waves from tuning forks with slightly different frequencies, resulting in the formation of beats.

05:00

📊 Graphical Representation of Beat Formation

The second paragraph delves into the graphical representation of beat formation using tuning forks as an example. It describes how the vibrations of two forks with slightly different frequencies, when superimposed, result in a pattern of compressions and rarefactions that vary over time. The paragraph illustrates how, at certain time intervals, the compressions and rarefactions align to produce either a minimum or maximum intensity of sound, thus forming beats. The example given involves two forks with frequencies of 6 Hz and 8 Hz, showing that the beats occur every half second, resulting in a beat frequency of 2 Hz. This visual method helps to understand the temporal pattern of sound intensity changes due to the superposition of two nearly similar frequency waves.

Keywords

💡Beats

Beats refer to the phenomenon where the intensity of sound alternates between maximum and minimum when two sound waves of nearly equal frequencies and amplitudes superimpose on each other. In the video's context, beats are central to understanding how sound waves interact and produce varying intensities, as demonstrated by the example of two sound sources with frequencies of 256 Hz and 260 Hz creating a beat frequency of 4 Hz.

💡Amplitude

Amplitude is the measure of the maximum extent of a vibration or oscillation, in this case, of a sound wave. It is a key factor in determining the intensity of the sound. The script mentions that for beats to occur, two waves must have equal amplitudes, which is crucial for the resulting sound's intensity to vary as they superimpose.

💡Frequency

Frequency is the number of complete oscillations of a wave that occur per unit of time, measured in Hertz (Hz). The video script discusses the importance of nearly equal frequencies for the formation of beats, as the difference in frequencies of the two sound sources determines the rate at which beats occur.

💡Superimpose

Superimposing, in the context of waves, means the act of placing two or more waves on top of each other so that their effects combine. The script explains that when two sound waves of nearly equal frequencies superimpose, they create the phenomenon of beats.

💡Intensity

Intensity of sound is related to the amplitude of the sound wave and is what the human ear perceives as the loudness of the sound. The video script describes how the intensity of the resultant sound at a particular position rises and falls alternately with time due to the superimposition of two sound waves.

💡Persistence of Hearing

Persistence of hearing is the property by which the impression of a sound persists in our mind for a short duration, approximately one-tenth of a second. The script uses this concept to explain why the difference in frequencies of two sound sources must be small enough for the brain to distinguish between them and perceive beats.

💡Beat Frequency

Beat frequency is the rate at which the intensity of the combined sound from two superimposed waves reaches a maximum and minimum alternately. It is equal to the difference in frequencies of the two original sounds. The script provides an example where the beat frequency is 4 Hz, which is the difference between 256 Hz and 260 Hz.

💡Fork A and Fork B

In the script, 'Fork A' and 'Fork B' are used as examples to illustrate the graphical method of understanding beats. They represent two sound sources with different frequencies, and their interaction is depicted to show how beats are formed when their waves superimpose.

💡Compression and Rarefaction

Compression and rarefaction are terms used to describe the regions of high and low pressure in a sound wave, respectively. In the script, these terms are used to describe the points of maximum and minimum pressure as the waves from Fork A and Fork B superimpose, leading to the formation of beats.

💡Graphical Method

The graphical method is a way to visually represent and understand the formation of beats by plotting the waves from two sound sources on a graph. The script uses this method to demonstrate how the superimposition of waves from Fork A and Fork B results in the periodic increase and decrease in sound intensity, forming beats.

💡Vibrations

Vibrations refer to the oscillations or back-and-forth movements that create sound waves. The script mentions the number of vibrations completed by Fork A and Fork B to illustrate the progression of their waves over time and how these vibrations contribute to the formation of beats.

Highlights

Beats occur when two sound waves of equal amplitudes and nearly equal frequencies superimpose on each other.

The intensity of the resultant sound at a particular position rises and falls alternately with time, creating beats.

Beats are formed when the intensity of sound is maximum at time T equals zero.

The time interval between two successive beats is called the beat frequency.

For distinct beats, the frequencies of the two sound sources should be nearly equal, with a difference less than 10 Hz.

The number of beats heard per second is equal to the difference in frequencies of the two incoming sounds.

The property of persistence of hearing explains why the frequency of beats must be less than 10 Hz.

A graphical method is used to illustrate the formation of beats using two tuning forks with different frequencies.

The superposition of waves from the two tuning forks results in the formation of beats.

The resultant wave is obtained by adding the waves from the two tuning forks according to the principle of superposition.

At certain time intervals, compressions from both forks align, resulting in maximum intensity of sound.

At other time intervals, compressions and rarefactions from the forks oppose each other, leading to minimum intensity of sound.

The number of beats per second is equal to the difference in frequencies of the two tuning forks.

The formation of beats demonstrates the interference of sound waves and the principle of superposition.

Understanding beats helps in studying the properties of sound waves and their interactions.

Beats have practical applications in tuning musical instruments and measuring sound frequencies.

Transcripts

beats beats in sound waves when two

waves of equal amplitudes and nearly

frequencies traveling in a medium along

the same direction superimpose on each

other the intensity of the resultant

sound at a particular position rises and

falls alternately with time this

phenomenon of alternate variation in the

intensity of sound with time at a

particular position when two sound waves

of nearly same frequencies and

amplitudes superimpose on each other is

called beats if intensity of sound is

maximum at time T equals to zero one

beat is said to be formed when intensity

becomes maximum again after becoming

minimum once in between the time

interval between two successive beats

that is two successive maximum of sound

is called

beat frequency for example when two

sounds of very close frequencies say 256

Hertz and two hundred sixty Hertz reach

and iya simultaneously we hear a sound

of frequency 258 Hertz which is the

average of two combining frequencies in

addition the intensity of sound heard

increases and decreases slowly the

number of beats heard per second is

equal to four which is the difference of

frequencies of two incoming sounds why

nearly equal frequencies for baits for

the formation of distinct beats

frequencies of do sources of sound

should be nearly equal

that is difference in inner frequencies

of two sources must be small say less

than ten this can be explained in terms

of the property of persistence of

hearing the impression of a sound heard

by our ears persist on our mind for one

tenth of a second if another sound is

heard before one tenth of a second

passes the impression of this two sounds

mix up and our mind cannot distinguish

between the two in order to hear

distinct beats time interval between two

successive beats must be greater than

one tenth of a second therefore

frequency of beats must be less than ten

is number of beats per second which is

equal to difference in frequencies of

two sources must be less than ten hence

the two sources should be nearly equal

frequencies formation of beats a

graphical method suppose we have two

turning folks a and B let the

frequencies of fork a be six and

frequency of fork be the eighth let the

waves of compression and rarefaction

given by the folks a and B be

represented by curves a and B

respectively in these curves a crest

represents a compression and the trough

represents a rarefaction

shown superimposition of the two waves

from fok's a and b we have represented

the resultant wave according to the

principle of superposition one in t

equals to 1/4 of a second a completes

six by four equals to 1 1 by 2

vibrations consisting of compression

rarefaction and a compression be

completes 8 by 4 equals to 2 vibrations

consisting of compression rarefaction

compression and rarefaction

does a rare affection due to a would

fall on compression due to be the

resultant would become minimum and hence

intensity of sound would be minimum at

q2 in T equals to 1/2 second a completes

6 by 2 equals to 3 vibrations consisting

of compression rarefaction compression

rarefaction compression and rarefaction

v completes a by 2 equals to 4

vibrations consisting of compression

rarefaction compression rarefaction

compression rarefaction compression and

rarefaction thus compression due to a

would fall on compression due to be the

resultant amplitude would become maximum

and hence resultant intensity of sound

would be maximum at are thus one beat is

formed in half second between P and R

similarly another beat is formed in the

next half second between R and T hence

number of beats per second is equal to

two which is also the difference in

frequencies of the two folks a and B