<< 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!

Guitar

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.

Piano

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

which gas is ideal gas
ANAMIKA Reply
how to calculate emf when you are given two circuits with different external resistance, current but no internal resistance?
Andiswa Reply
you have to find the current of whole both circuits nd add em...
Amanzialwandle
calculate the distance between two charge +4nc and -3nc if electrostatic is 0.005N
Malaza Reply
use the coulombs law equation where there is F u substite by 0.005 then u cross multiple
Neldo
what is atomic
motheo Reply
what is charge
motheo
how to calculate the distance between Q1 and point P if you are given distance between point P and Q2
Lwando Reply
how do we calculate the magnitude of the force between two objects
Ntombi Reply
we use Newtons law ...fnet=ma
Fikile
how do you calculate the enery change in enthalpy reaction, can someone explain it to me guys
Buyie Reply
∆H(enthalpy change)= Hproducts- Hreactants.... use this formula, H stands for enthalpy which is regarded as energy
Andiswa
atomic model john dalton
Alliieyza Reply
Hlw,, I want to join.
crippah
what is a normal force
tumelo Reply
normal force is the line that is perpendicular to the surface
Thabo
normal force is the force exerted to an object by the surface , perpendicular to the surface
Fhatani
I want to join
Londiwe
better explanation of FARADAY'S LAW OF INDUCTION
Kgaugelo
what is the formular of energy
Wilka Reply
E=f\q
Wonder
E=hf
Mondli
doesnt it like depend on the type of energy
Benjamin
what does (1s2 2s2 and 2p6) mean?
Ryan Reply
That is Albau Diagram I guess!! it represent number of electrons in each energy orbit!! the numbers 1s, 2s&2p, 3s and so on represent energy orbit and then the other numbers after s & p represent number of electrons
Andiswa
That is SP notation
Kgaugelo
What are the differences between pd and emf?
Santosh Reply
How to calculate magnitude of Friction force
Tanaka Reply
in Newton
Obakeng
yeh
Obakeng
in newton
Fikile
Onother Question?
crippah
yes bruh
Fikile
First of all in wat Grade ae u..?
crippah
grde 11
Fikile
Oka nd hw is the properties of a substance afected by the intermoleculaer forces...
crippah
hi guys I m in grade 11 I need help with electrostatics
Serati
what is newton
Ndamulelo Reply
look for the x components n y components then after y add the x components separate n y separate then u use the Pythagoras theorem 2 find the resultand
Abigail Reply
Thank you very much
Luvuyo
how do I find 🔍 the critical angle
Ntandokazi
angle of incident and angle of reflection must always approach normal line thats where u will see 90° which is critical point
Tumelo

Get the best Siyavula textbooks: gr... course in your pocket!





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?

Ask