Two Chapter 10

· When tuning forks of different frequency sound simultaneously, the sound will alternate between loud and soft (beat)

· Beats - periodic changes in sound intensity.

· Because wavelengths and frequencies are different, at one location in space, sometimes a rarefaction meets a compression, which results in destructive interference (soft sound). At other times, two compressions or rarefactions meet to produce constructive interference (loud sound).

· As time goes by, at a point in space, constructive and destructive interference alternate and produce the beats.

· Beat Frequency (Bf) - The number of maximum intensity points that occur per second

Bf = |f₂ - f₁|

· Beats are used to tune instruments. When sounded simultaneously, if there are no beats, the two instruments are in tune.

· Vibrating strings produce sound.

· The frequency of the sound depends upon

o diameter of the string (d)

o density of the material making up the string (e)

o length of the string (L)

o tension (T)

· The relationship between these factors and frequency is summarized by the following equation.

· This equation is used for designing musical instruments.

o E.G. For a piano, the treble strings are at high tension. Bass strings are wound with string to increase mass and density. By making these adjustments, the range of length of strings needed to produce the range of notes is reduced.

· With vibrating strings, waves moving down the string in either direction may interfere with each other and produce standing waves.

· These standing waves will have nodes at each end where the string is attached.

· Different frequencies can be on the string depending upon the number of loops and nodes.

· More than one frequency can be present at a time.

o Stringed instruments produce the fundamental frequency with many overtones superimposed on the fundamental.

· The quality of an instrument depends upon the number and intensity of overtones produced with the fundamental.

o The fundamental frequency sets the pitch of a note, and the type of sound (violin or piano etc.) is determined by the overtones present.

· Synthesizers duplicate the sound of an instrument by placing the overtones for that instrument onto the fundamental.

· Every object has a natural frequency at which it will vibrate.

o E.G. A swing requires a push at the proper time to increase amplitude.

· Natural frequency - resonant frequency

o determined by the dimensions of the object (usually length)

§ E.G. A swing requires a push at the proper time to increase amplitude. (i.e.: push occurs at a frequency = natural frequency.

· Resonance - The response of an object, (free to vibrate) to a periodic force with the same frequency as the natural frequency of the object.

· Mechanical resonance - The response of an object where there is physical contact between the periodic force and the vibrating object.

· A swings - causes E to swing but not the others

· B swings - causes D to swing but not the others

· C swings - no other one will swing.

• With A, for example, when it swings, it transmits a periodic force to B, C, D, and E. This periodic force occurs only at E's natural frequency. As a result, E begins to move, and the amplitude of its swing builds up. The others will move too, but sometimes the applied force will add to the objects amplitude of swing, and sometimes it will subtract from the amplitude of swing. These objects (B,C, and D) will therefore not build up large amplitude swings.
• Natural frequency must be taken into consideration when designing structures or the structure may collapse.

E.G. Tacoma Bridge collapse.

Soldiers on a bridge.

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November 18, 2013