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High school physics
Course: High school physics > Unit 10
Lesson 3: Beats and interference of sound wavesBeat frequency
Beat frequency occurs when two waves with different frequencies overlap, causing a cycle of alternating constructive and destructive interference between waves. Learn how this results in a fluctuation in sound loudness, and how the beat frequency can be calculated by finding the difference between the two original frequencies. Created by David SantoPietro.
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- The higher a note, the higher it's frequency. We've established that different frequencies when played together creates "wobbles" due to constructive and destructive interference. But normally musicians don't play the same exact note together; they play different notes with different frequencies together. So does that mean when musicians play harmonies, we hear "wobbles", and the greater the difference in interval, the more noticeable the "wobbling"?(11 votes)
- that happens. when you tune a piano, the harmonics of notes can create beats. higher harmonics mean more beats, because the same percentage of difference results in more units difference when scaled up.(2 votes)
- but if the difference in frequency of 2 instruments is really high, so the beat frequency would be really high and human ear would not recognize any wobbling, it would seem that its one continuos note, am I right?(8 votes)
- Hello Dean,
Yes and no. Each of us comes equipped with incredible music processor between our ears, With a little training we are able to detect these beat. We can use this ability to tune an instrument, in fact a trained musician can tune in real time by making thousands of minor adjustments.
Suppose we had two tones. Lets' keep one at a constant frequency and let's let the other one constantly increase. When we start the tones are the same, as we increase we start hear the beat frequencies - it will start slow and then get faster and faster.
Keep going and something interesting happens. We will perceive beat frequencies once again as the tones approach certain mathematic relationships. As an example consider western musical terms. If we start at "C" we will hear strong beats when approaching "E" and again at "G."
Regards,
APD(6 votes)
- So is the amplitude of a sound wave what we use to measure the loudness?(6 votes)
- Audio engineer/music producer here. Yes and no.
Yes amplitude is what we would use to mechanically measure the loudness of a given sound wave.
However sometimes two sounds can have the sample amplitude, but due to their harmonics one can be PERCEIVED as louder than the other. The human ear is more sensitive to certain frequencies than to others as given by the Fletcher-Munson curve.(8 votes)
- Can we create 2 perfectly destructive waves at home?
If so how? If we cannot,why?(6 votes) - When two instruments producing same frequency sound, there must be a chance that two sound wave are out of phase by pi and cancel each other out.
Why would this seem never happen?(5 votes)- by 90 degrees off, then you can. it is just that it is too hard to time it right, unless a computer can play 2 equal tones with a set phase interval between them.(3 votes)
- What happens when we use a second sound with a different amplitude as compared to the first one?(4 votes)
- The formation of beats is mainly due to frequency. If the amplitude of the two waves are not equal, than the overall sound will vary between a maximum and a minimum amplitude but will never be zero. The points at which in the equal amplitude case we were getting zero resultant wave, we will have some uncancelled part of the wave with a higher frequency(2 votes)
- What would happen if a wave was overlapped with another wave that had the half of its wavelength? How would that sound?
Hope my question makes sense.(3 votes)- The sound would be the one you hear if you play both waves separatly at the same time. If you want to see the wave, it looks like this: https://www.khanacademy.org/computer-programming/sin-waves/4604911313551360(2 votes)
- Hi
I have a question about example clarinet
Iwant to know why don't we tune down 445Hz to 440Hz, i think it very good to do it. But why we use the method that tune up from 435Hz to 440Hz. Because, if you intepret same as this video, I think if we successive raise from 445Hz, it still have more beat per second.
Hope you reply soon!(3 votes) - Hi! I have a question: since the wave travels up and down, what does it mean when the distance from the midline to the trough is negative? is because that the molecule is moving back and forth, so positive means it moves forward and negative means the molecule goes backwards? It doesn't mean that the volume decreases right?? I would rlly appreciate it if someone could clarify this point for me! :)(3 votes)
- your intuition is right
air molecules moving to the right = positive on wave graph
left = negative
absolute height (whatever the sign is) = volume (amplitude) of the sound(1 vote)
- At, he says 'peak to peak' but isn't that peak to trough? 1:19
Also can I interpret the second wave as a second 'cause' of displacement acting on the same air particle (same point in space), and the combine wave the result of the 'net cause'?(2 votes)
Video transcript
- [Voiceover] What's up everybody? I wanna talk to you about beat frequency, and to do so let me talk to you about this air displacement
versus time graph. So this is gonna give you the displacement of the air molecules for any
time at a particular location. So say you had some
speaker and it was playing a nice simple harmonic
tone and so it would sound something like this. (tone playing) That's 440 hertz, turns
out that's an A note. People use that a lot when
they're tuning instruments and whatnot so that's this
sound would sound like, and let's say it's sending this sound out and at a particular
point, one point in space, we measure what the
displacement of the air is as a function of time. Let's just say we're three meters to the right of this speaker. Just so we have a number to refer to, so there's air over
here, the air's chillin, just relaxin and then
the sound wave comes by and that causes this air to get displaced. It moves back and forth. A minuscule amount but some amount, and if we graphed that displacement as a function of time
we would get this graph. So in other words this entire graph is just personalized
for that point in space, three meters away from this speaker. So why am I telling you this? Well because we know if
you overlap two waves, if I take another wave and
let's just say this wave has the exact same
period as the first wave, right so I'll put these peak to peak so you can see, compare the peaks, yep. Takes the same amount of time for both of these to go through a cycle, that means they have the same period, so if I overlap these,
in other words if I took another speaker and I played
the same note next to it, if I played it like this I'd
hear constructive interference cause these are overlapping peak to peak, valley to valley perfectly. This note would get louder
if I was standing here and listening to it and it
would stay loud the whole time. It would just sound
louder the entire time, constructive interference, and if I moved that speaker
forward a little bit or I switched the leads,
if I found some way to get it out of phase so that it was destructive interference, I'd hear a softer note,
maybe it would be silent if I did this perfectly and
it would stay silent or soft the whole time, it would stay
destructive in other words. So if you overlap two waves
that have the same frequency, ie the same period, then
it's gonna be constructive and stay constructive, or be destructive and stay destructive, but
here's the crazy thing. Let me get rid of this. What if we overlapped two waves
that had different periods? What would happen then? Let's just try it out. So let me take this wave, this
wave has a different period. Look it, if I compare these two peaks, these two peeks don't line up, if I'm looking over here the distance between these two peaks is not the same as the distance between these two peaks. It's hard to see, it's almost the same, but this red wave has a
slightly longer period if you can see the time between peaks is a little longer than
the time between peaks for the blue wave and you might think, "Ah there's only a little difference here. "Can't be that big of a deal right?" It kind of is. It causes a new phenomenon
called beat frequency, and I'll show you why it happens here. So if I overlap these two. So now you take two speakers, but the second speaker you play it at a slightly different
frequency from the first. What would you get? Let's just look at what happens over here. They start out in phase
perfectly overlapping, right? Peak to peak, so this is constructive, this wave starts off constructively interfering with the other wave. So you hear constructive interference, that means if you were
standing at this point at that moment in time, notice
this axis is time not space, so at this moment in time right here, you would hear constructive interference which means that those
waves would sound loud. Sound really loud at that moment, but then you wait, this red
waves got a longer period. So it's taking longer for this red wave to go through a cycle, that means they're gonna start becoming out of phase, right? The peaks aren't gonna line up anymore. When this blue wave has displaced the air maximally to the right, this red wave is gonna
not have done that yet, it's gonna take a little longer
for it to try to do that. So these become out of phase,
now it's less constructive, less constructive, less constructive, over here look it, now the
peaks match the valleys. This is straight up
destructive, it's gonna be soft, and if you did this perfectly it might be silent at that point. You wait a little longer
and this blue wave has essentially lapped
the red wave, right? You waited so long the
blue wave has gone through an extra whole period
compared to the red wave, an so now the peaks line up again, and now it's constructive again because the peaks match the peaks and the valleys match the valleys. So at that point it's constructive and it's gonna be loud
again so what you would hear if you were standing at this
point three meters away, you'd first at this moment in
time hear the note be loud, then you'd hear it become soft and then you'd hear it become loud again. You'd hear this note wobble, and the name we have for this phenomenon is the beat frequency or
sometimes it's just called beats, and I don't mean you're
gonna hear Doctor Dre out of this thing that's
not the kind of beats I'm talking about, I'm just talking about that wobble from louder
to softer to louder. Actually let me just play it. Let me show you what this sounds like. So if we play the A note again. (tone playing) That's the A note. Let me play, that's 440 hertz, right? That's a particular frequency. Let me play just a slightly
different frequency. I'll play 443 hertz. (tone playing) And you're probably like that just sounds like the exact same thing,
I can't tell the difference between the two, but if I play them both you'll definitely be able
to tell the difference. So I'm gonna play them both now. Here's the 443 hertz, and here's the 440. (two tones playing) And you hear a wobble. This thing starts to wobble. So let me stop this. So that's what physicists
are talking about when they say beat frequency or beats, they're referring to that wobble and sound loudness that you hear when you overlap two waves
that different frequencies. This is important, it only works when you have waves of
different frequency. So what if you wanted to know
the actual beat frequency? What if you wanted to know how many wobbles you get per second? So how often is it going from constructive to destructive back to constructive? If that takes a long time the
frequency is gonna be small, cause there aren't gonna
be many wobbles per second, but if this takes a short amount of time, if there's not much time
between constructive back to constructive
then the beat frequency's gonna be large, there will
be many wobbles per second. How would you figure
out this beat frequency, I'll call it FB, this
would be how many times this goes from constructive
back to constructive per second. So if it does that 20 times per second, this thing would be
wobbling 20 times per second and the frequency would be 20 hertz. So how do you find this if you know the frequency of each wave, and it turns out it's very very easy. I'm just gonna show you
the formula in this video, in the next video we'll derive it for those that are interested, but in this one I'll
just show you what it is, show you how to use it. So the beat frequency
if you wanna find it, if I know the frequency of the first wave, so if wave one has a frequency, f1. So say that blue wave has a frequency f1, and wave two has a frequency f2, then I can find the beat frequency by just taking the difference. I can just take f1 and then subtract f2, and it's as simple as that. That gives you the beat frequency. Now you might wonder like wait a minute, what if f1 has a smaller
frequency than f2? That would give me a
negative beat frequency? That doesn't make sense we
can't have a negative frequency so we typically put an absolute
value sign around this. You should take the higher
frequency minus the lower, but just in case you don't just stick an absolute value and that gives you the size of this beat frequency, which is basically the
number of wobbles per second, ie the number of times
it goes from constructive all the way back to
constructive per second. That's what this beat frequency means and this formula is how you can find it. Now I should say to be clear, we're playing two different sound waves, our ears really just sort of
gonna hear one total wave. So these waves overlap. You can do this whole analysis
using wave interference. You write down the equation of one wave, you write down the
equation of the other wave, you add up the two, right? We know that the total wave is gonna equal the summation of each wave at
a particular point in time. So at one point in time if we take the value of each wave and add them up, we'd get the total wave,
what would that look like? What would the total wave look like? It would look like this. If we just add it up
you'd get a total wave that looks like this
green dashed wave here. Right over here, they
add up to twice the wave, and then in the middle they
cancel to almost nothing, and then back over here they add up again, and so if you just
looked at the total wave, it would look something like this. So the total wave would
start with a large amplitude, and then it would die out because
they'd become destructive, and then it would become
a large amplitude again. So you see this picture a lot when you're talking about beat frequency because it's showing what the total wave looks like as a function of time when you add up those two individual waves since this is going from constructive to destructive to constructive again, and this is why it sounds loud and then soft and then
loud again to our ear. So what would an example
problem look like for beats? Let's say you were told
that there's a flute, and let's say this flute
is playing a frequency of 440 hertz like that
note we heard earlier, and let's say there's also a clarinet. They play it, they wanna
make sure they're in tune, they wanna make sure
they're jam sounds good for everyone in the audience, but when they both try to play the A note, this flute plays 440, this
clarinet plays a note, and let's say we hear a beat frequency, I'll write it in this color,
we hear a beat frequency of five hertz so we hear
five wobbles per second. In fact if you've ever
tried to tune an instrument you know that one way to tune it is to try to check two notes that are
supposed to be the same. You can tell immediately
if they're not the same cause you'll hear these wobbles, and so you keep tuning it until you don't hear the wobble anymore. As those notes get closer and closer, there'll be less wobbles per second, and once you hear no wobble at all, you know you're at the
exact same frequency, but these aren't, these are off, and so the question might ask, what are the two possible
frequencies of the clarinet? Well we know that the beat frequency is equal to the absolute value of the difference in the two frequencies. So if there's a beat
frequency of five hertz and the flutes playing 440,
that means the clarinet is five hertz off from the flute. So the clarinet might
be a little too high, it might be 445 hertz,
playing a little sharp, or it might be 435 hertz,
might be playing a little flat. So we'd have to tune to figure out how it can get to the point where there'd be zero beat frequency, cause when there's zero
beat frequencies you know both of these frequencies are the same, but what do you do? How does it know? How does the clarinet
player know which one to do? You kind of don't sometimes. Sometimes you just have to test it out. Let's say the clarinet player assumed, all right maybe they were
a little too sharp 445, so they're gonna lower their note. So they start to tune down,
what will they listen for? They'll listen for less
wobbles per second. So if you become more in tune in stead of, (imitates wobbling tone) you would hear, (imitates slowing wobble) right, and then once
you're perfectly in tune, (hums tone) and it would be perfect,
there'd be no wobbles. If this person tried it and there were more wobbles per second
then this person would know, "Oh, I was probably at this lower note. "cause if I'm at 435, and
I go to say 430 hertz, "that's gonna be more out of tune." Now the beat frequency would be 10 hertz, you'd hear 10 wobbles per second, and the person would know immediately, "Whoa, that was a bad idea. "I must not have been too sharp. "I must've been too flat." So now that you know
you're a little too flat you start tuning the other way, so you can raise this up to 440 hertz and then you would hear
zero beat frequency, zero wobbles per second, a nice tune, and you would be playing in harmony. So recapping beats or
beat frequency occurs when you overlap two waves that
have different frequencies. This causes the waves to go from being constructive to destructive
to constructive over and over, which we perceive as a wobble
in the loudness of the sound, and the way you can
find the beat frequency is by taking the difference
of the two frequencies of the waves that are overlapping.