<< Chapter < Page Chapter >> Page >

You should have found this formula:

λ = 2 L n - 1

Here, n is the number of nodes. L is the length of the string. The frequency f is:

f = v λ

Here, v is the velocity of the wave. This may seem confusing. The wave is a standing wave, so how can it have a velocity? But one standing wave is made up of many waves that travel back and forth on the string.Each of these waves has the same velocity. This speed depends on the mass and tension of the string.

We have a standing wave on a string that is 65 cm long. The wave has a velocity of 143 m.s - 1 . Find the frequencies of the fundamental, first, second, and third harmonics.

  1. L = 65 cm = 0 . 65 m v = 143 m . s - 1 f = ?

    To find the frequency we will use f = v λ

  2. To find f we need the wavelength of each harmonic ( λ = 2 L n - 1 ). The wavelength is then substituted into f = v λ to find the harmonics. The table below shows the calculations.

    110 Hz is the natural frequency of the A string on a guitar. The third harmonic, at 440 Hz, is the note that orchestras use for tuning.

Got questions? Get instant answers now!


Guitars use strings with high tension. The length, tension and mass of the strings affect the pitches you hear.High tension and short strings make high frequencies; low tension and long strings make low frequencies. When a string is first plucked, it vibrates at many frequencies.All of these except the harmonics are quickly filtered out. The harmonics make up the tone we hear.

The body of a guitar acts as a large wooden soundboard. Here is how a soundboard works: the body picks up the vibrations of the strings. It then passes these vibrations to the air.A sound hole allows the soundboard of the guitar to vibrate more freely. It also helps sound waves to get out of the body.

The neck of the guitar has thin metal bumps on it called frets. Pressing a string against a fret shortens the length of that string.This raises the natural frequency and the pitch of that string.

Most guitars use an "equal tempered" tuning of 12 notes per octave. A 6 string guitar has a range of 4 1 2 octaves with pitches from 82.407 Hz (low E) to 2093 kHz (high C). Harmonics may reach over 20 kHz, in the inaudible range.


Let us look at another stringed instrument: the piano. The piano has strings that you cannot see. When a key is pressed, a felt-tipped hammer hits astring inside the piano. The pitch depends on the length, tension and mass of the string. But there are many more strings than keys on a piano. This is because the short and thinstrings are not as loud as the long and heavy strings. To make up for this, the higher keys have groups of two to four strings each.

The soundboard in a piano is a large cast iron plate. It picks up vibrations from the strings. This heavy plate can withstand over 200 tons of pressure from string tension!Its mass also allows the piano to sustain notes for long periods of time.

The piano has a wide frequency range, from 27,5 Hz (low A) to 4186,0 Hz (upper C). But these are just the fundamental frequencies. A piano plays complex,rich tones with over 20 harmonics per note. Some of these are out of the range of human hearing. Very low piano notes can be heard mostly because of their higher harmonics.

Questions & Answers

what is the difference between intramolecular and intermolecular forces
Xiluva Reply
please help me here how do the molecular masses of the compounds change?
Khutso Reply
how to calculate atom mass
Mbali Reply
how do water molecules form
Mukonazwothe Reply
water molecules consist of two atoms of hydrogen linked by covalent bonding to the same atom of oxygen ...hydrogen bonds are formed easily when two water molecules come close together , but are easily broken when the water molecule moves apart again
similarity between vander waals forces and hydrogen bond
Angel Reply
type of intermolecular forces between 2 hydrogen and 2 oxygen
when an atom X of an element in Group 1 reacts to become X+
Rhulani Reply
You have O.5 dm^3 of a KNO3 solution of concentration 0.2 M .You need to dilute this solution to get a solution of concentration 0.18M. calculate how many cubic cm of H2O you need to achieve this
Thimna Reply
im really struggling with this question please help me
what is a radium
Zieniengie Reply
when 3.22 moles ofAl react with 4.96 moles HBr, how many moles of H2 are formed?
Devina Reply
how can we calculate the displacement?
Etaya Reply
can u tell me how to understand newtons law
Mutandanyi Reply
well they are many way to understand newtons but my way of understand it is to look every object around and think of what type of law has been applied in that object but fist state the law so you can get use to it
what is matter
Mutandanyi Reply
matter is any thing that has mass and occupy space
newton's first law of motion
Modiehii Reply
how to calculate resultant?
Future Reply
resultant of what?
ohm law
Ohm's Law
how do you calculate magnitude of acceleration
Hlolohelo Reply
u use the formula fnet equal mass

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now

Source:  OpenStax, Siyavula textbooks: grade 11 physical science. OpenStax CNX. Jul 29, 2011 Download for free at http://cnx.org/content/col11241/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Siyavula textbooks: grade 11 physical science' conversation and receive update notifications?