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The lowest frequency, called the fundamental frequency    , is thus for the longest wavelength, which is seen to be λ 1 = 2 L size 12{λ rSub { size 8{1} } =2`"L"} {} . Therefore, the fundamental frequency is f 1 = v w / λ 1 = v w / 2 L size 12{f rSub { size 8{1} } =v rSub { size 8{w} } /λ rSub { size 8{1} } =v rSub { size 8{w} } /2`"L"} {} . In this case, the overtones    or harmonics are multiples of the fundamental frequency. As seen in [link] , the first harmonic can easily be calculated since λ 2 = L size 12{λ rSub { size 8{2} } =L} {} . Thus, f 2 = v w / λ 2 = v w / 2 L = 2 f 1 size 12{f rSub { size 8{2} } =v rSub { size 8{w} } /λ rSub { size 8{2} } =v rSub { size 8{w} } /2`"L"=2f rSub { size 8{1} } } {} . Similarly, f 3 = 3 f 1 size 12{f rSub { size 8{3} } =3f rSub { size 8{1} } } {} , and so on. All of these frequencies can be changed by adjusting the tension in the string. The greater the tension, the greater v w size 12{v rSub { size 8{w} } } {} is and the higher the frequencies. This observation is familiar to anyone who has ever observed a string instrument being tuned. We will see in later chapters that standing waves are crucial to many resonance phenomena, such as in sounding boxes on string instruments.

The graph shows a wave with wavelength lambda one equal to L, which has two loops. There three nodes and two antinodes in the figure. The length of one loop is L.
The figure shows a string oscillating at its fundamental frequency.
first overtone is shown as the wave length if lambda two is L and there are three nodes and two antinodes in the figure. For first overtone the frequency f two is equal to two times f one.
First and second harmonic frequencies are shown.

Beats

Striking two adjacent keys on a piano produces a warbling combination usually considered to be unpleasant. The superposition of two waves of similar but not identical frequencies is the culprit. Another example is often noticeable in jet aircraft, particularly the two-engine variety, while taxiing. The combined sound of the engines goes up and down in loudness. This varying loudness happens because the sound waves have similar but not identical frequencies. The discordant warbling of the piano and the fluctuating loudness of the jet engine noise are both due to alternately constructive and destructive interference as the two waves go in and out of phase. [link] illustrates this graphically.

The graph shows the superimposition of two similar but non-identical waves. Beats are produced by alternating destructive and constructive waves with equal amplitude but different frequencies. The resultant wave is the one with rising and falling amplitude over different intervals of time.
Beats are produced by the superposition of two waves of slightly different frequencies but identical amplitudes. The waves alternate in time between constructive interference and destructive interference, giving the resulting wave a time-varying amplitude.

The wave resulting from the superposition of two similar-frequency waves has a frequency that is the average of the two. This wave fluctuates in amplitude, or beats , with a frequency called the beat frequency    . We can determine the beat frequency by adding two waves together mathematically. The result,

f B = f 1 f 2 size 12{f rSub { size 8{B} } = lline f rSub { size 8{1} } - f rSub { size 8{2} } rline } {}

is the beat frequency. The resultant wave has the average frequency of the two superimposed waves, but it also fluctuates in overall amplitude at the beat frequency f B size 12{f rSub { size 8{"B"} } } {} . This result is valid for all types of waves. However, if it is a sound wave, providing the two frequencies are similar, then what we hear is an average frequency that gets louder and softer (or warbles) at the beat frequency.

Making career connections

Piano tuners use beats routinely in their work. When comparing a note with a tuning fork, they listen for beats and adjust the string until the beats go away (to zero frequency). For example, if the tuning fork has a 256 Hz size 12{"256"``"Hz"} {} frequency and two beats per second are heard, then the other frequency is either 254 size 12{"254"} {} or 258 Hz size 12{"258"`"Hz"} {} . Most keys hit multiple strings, and these strings are actually adjusted until they have nearly the same frequency and give a slow beat for richness. Twelve-string guitars and mandolins are also tuned using beats.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Concepts of physics with linear momentum. OpenStax CNX. Aug 11, 2016 Download for free at http://legacy.cnx.org/content/col11960/1.9
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