1. 13-3 harmonics Understand standing wave and harmonics
Understand Interference and Beats

2. Standing Wave Patterns and harmonics
All objects have a frequency or set of frequencies with which they naturally vibrate when struck, plucked, strummed or somehow disturbed. Each of the natural frequencies at which an object vibrates is associated with a standing wave pattern.
A standing wave pattern is created within a medium when the reflected waves from one end of the medium interfere with incident waves from the source, The result of the interference is that specific points along the medium appear to be standing still while other points vibrated back and forth. Such patterns are only created within the medium at specific frequencies of vibration. These frequencies are known as harmonic frequencies or merely harmonics. At any frequency other than a harmonic frequency, the interference of reflected and incident waves results in a disturbance of the medium that is irregular and non-repeating.

3. The natural frequencies of an object are merely the harmonic frequencies at which standing wave patterns are established within the object. These standing wave patterns represent the lowest energy vibrational modes of the object.

4. Harmonics are integral multiples of the fundamental frequency.
Fundamental frequency is the lowest frequency of vibration of a standing wave.
Harmonic series is a series of frequencies that includes the fundamental frequency and integral multiples of the fundamental frequency.
For example, the harmonic series can include: 64 Hz, 128 Hz, 256 Hz, 516 Hz …
Fundamental frequency determines pitch
Harmonic series depends on the length of the string:

5. Sound Reflection - echo or a reverberation.
A reverberation often occurs in a small room with height, width, and length dimensions of approximately 17 meters or less. The reflected sound wave has a very short delay, it seems to the person that the sound is prolonged. You might observe reverberations when talking in an empty room, when honking the horn while driving through a highway tunnel or underpass, or when singing in the shower.
Echoes occur when a reflected sound is perceived as a second sound rather than the prolonging of the first sound.

6. Sound Interference and Beats
When sound waves meet, interference occurs. The interference causes the medium to take on a shape which results from the net effect of the two individual waves upon the particles of the medium.
Constructive interference occurs if compression meets up with compression and rarefaction meets up with rarefaction. Constructive interferences produce a anti-node, results a louder sound.
Destructive interference occurs if compression of one wave meets the rarefaction of another wave. Destructive interference produce a node, results no sound at all.
..\..\sound_en.jar

7. Destructive interference of sound waves is an important issue in the design of concert halls and auditoriums. One means of reducing the severity of destructive interference is by the design of walls, ceilings, and baffles that serve to absorb sound rather than reflect it.
The destructive interference of sound waves can also be used advantageously in noise reduction systems. Ear phones have been produced which can be used by factory and construction workers to reduce the noise levels on their jobs. Such ear phones capture sound from the environment and use computer technology to produce a second sound wave which one-half cycle out of phase. The combination of these two sound waves within the headset will result in destructive interference and thus reduce a worker's exposure to loud noise.

8. Musical Beats
When sound waves with slightly different frequencies traveling in the same direction, the effect of interference is perceived as a variation in loudness, called beats.
Note: the diagrams represents a sound wave by a sine wave. Because the variations in pressure with time take on the pattern of a sine wave. Sound is not a transverse wave, sound is a longitudinal wave.

9. The beat frequency refers to the number of beats per second
The beat frequency refers to the number of beats per second. For example, if two complete cycles of high and low volumes are heard every second, the beat frequency is 2 Hz. The beat frequency equals to the difference in frequencies of the two interfering notes.
For example, if two sound waves with frequencies of 256 Hz and 254 Hz are played simultaneously, a beat frequency of 2 Hz will be detected.

10. Lab - Harmonic Frequencies
Overview: in order to produce a standing wave, certain conditions must be satisfied. For example, to produce a standing wave in a given string with length l, certain wavelength must be fulfilled.
Purpose (5 pt): To determine the mathematical relationship between the wavelengths of various harmonics and the length of the string in a standing wave.
Material (5 pt): Computer, physics classroom website
Procedure: go to
set length = 200 cm; amplitude = 20 cm
change the harmonic # and record the # of harmonics, stand wave pattern, length of the string and wavelength
Data (20 pt): includes a table with column headings: harmonic number, standing wave pattern, and frequency.
Conclusion (20 pt) includes a couple of sentences and an equation which responds to the purpose of the lab; symbols used within the equation are clearly defined. The Discussion of Results should explain how the collected data are consistent with the equation written in the Conclusion. Specific rows of the table should be referenced and discussed in an effort to show how the equation fits the data.

11. length of the string (cm)
# of harmonics
stand wave pattern
length of the string (cm)
Wavelength (m)
Frequency (Hz)
Speed (m/s) 1 2 3 4 5 6