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What is your favorite musical instrument? How do you play it? Do you pluck a string, like a guitar? Do you blow through it, like a flute? Do you hit it, like a drum?All musical instruments work by making standing waves. Each instrument has a unique sound because of the special waves made in it. These waves could be in the strings of a guitar or violin.They could also be in the skin of a drum or a tube of air in a trumpet. These waves are picked up by the air and later reach your ear as sound.

In Grade 10, you learned about standing waves and boundary conditions. We saw a rope that was:

  • fixed at both ends
  • fixed at one end and free at the other

We also saw a pipe that was:

  • closed at both ends
  • open at both ends
  • open at one end, closed at the other

String and wind instruments are good examples of standing waves on strings and pipes.

One way to describe standing waves is to count nodes. Recall that a node is a point on a string that does not move as the wave changes.The anti-nodes are the highest and lowest points on the wave. There is a node at each end of a fixed string. There is also a node at the closed end of a pipe.But an open end of a pipe has an anti-node.

What causes a standing wave? There are incident and reflected waves traveling back and forth on our string or pipe. For some frequencies, these waves combine in just the right way so that the whole wave appears to be standing still.These special cases are called harmonic frequencies, or harmonics . They depend on the length and material of the medium.


A harmonic frequency is a frequency at which standing waves can be made in a particular object or on a particular instrument.

Standing waves in string instruments

Let us look at a basic "instrument": a string pulled tight and fixed at both ends. When you pluck the string, you hear a certain pitch. This pitch is made by a certain frequency.What causes the string to emit sounds at this pitch?

You have learned that the frequency of a standing wave depends on the length of the wave. The wavelength depends on the nodes and anti-nodes.The longest wave that can "fit" on the string is shown in [link] . This is called the fundamental or natural frequency of the string. The string has nodes at both ends. The wavelength of the fundamental is twice the length of the string.

Now put your finger on the center of the string. Hold it down gently and pluck it. The standing wave now has a node in the middle of the string. There are three nodes.We can fit a whole wave between the ends of the string. This means the wavelength is equal to the length of the string.This wave is called the first harmonic. As we add more nodes, we find the second harmonic, third harmonic, and so on.We must keep the nodes equally spaced or we will lose our standing wave.

Harmonics on a string fixed at both ends.

Investigation : waves on a string fixed at both ends

This chart shows various waves on a string. The string length L is the dashed line.

  1. Fill in the:
    • number of nodes
    • number of anti-nodes
    • wavelength in terms of L
    The first and last waves are done for you.
    Wave Nodes Antinodes Wavelength
  2. Use the chart to find a formula for the wavelength in terms of the number of nodes.

Questions & Answers

explain why HCL is a Bronstead lowry acid . use an equation of HCL in water to explain
Mihlali Reply
what is electron. ( you should not allowed to tell it properties in it defination.)
vigyan Reply
a charged particle.
investigative question
Obakeng Reply
how do you create a bomb
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if you want to create bomb use this chemical substance oxidised, sulphuric acid,tobacco,gas and flammable substance , mix all this substance together and put in strong mental bottle like gas bottle put in . you must close the bottle very parked and carry that bottle carefully and shake in 5 minutes
after shake put this bottle were the temperature is 100 degrees Celsius after moment that bottle will be high explosion like bomb
what is mass
asmerom Reply
is object amount matter contain by object
what is hypothesis
hypothesis is a tentative explanation that does not have facts and it can be proven to be wrong or right
wath is physical science
Siphelo Reply
what is physics
Dineo Reply
the branch of science concerned with the nature and properties of matter and energy
use a vector scale diagram and represent the two displacements(5m east and 7m west)
itumeleng Reply
what os covalent?
Shellah Reply
can i ask something?
Uapfa Reply
how to calculate enthalpy on a reaction?
how do you learn this chapter festet
Lisakhanya Reply
it's not all about learning it fast but understanding the basics, the concepts. formulas .. if you juss understand the basics you know the chapter .understand it
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can i ask smething.?
electric field around a point
Sameer Reply
The force per positive unit charge
what is Kevlar made of ?
Crazy Reply
How do I determine the number of valence electrons for an atom
Kamohelo Reply
look at its group number on periodic table. group 2 elements will have 2 valence electrons and so on for all the groups. (correct me if I'm wrong but this is how I remeber it )
how to find a point between to charges that is zero?
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Source:  OpenStax, Siyavula textbooks: grade 11 physical science. OpenStax CNX. Jul 29, 2011 Download for free at http://cnx.org/content/col11241/1.2
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