Beats in Sound Waves
Summary
TLDRThe 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
🎵 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.
📊 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.
Mindmap
Keywords
💡Beats
💡Amplitude
💡Frequency
💡Superimpose
💡Intensity
💡Persistence of Hearing
💡Beat Frequency
💡Fork A and Fork B
💡Compression and Rarefaction
💡Graphical Method
💡Vibrations
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
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