11/30/15

Resonance

Oscillation of a system to a preferential frequency causing the system to achieve a greater amplitude then its oscillation.

ExamplesSwing set

Lasers

See for yourself

With your group come and grab a slinky and vibrate it at different frequencies. Notice what happens at the resonant frequency and if you vibrate at slightly slower and higher frequencies.

Tacoma Narrows Bridge

Resonance happens in nature frequently. Music, watches, electrons. However, one disastrous effect of not taking resonance into account is the Tacoma Narrows Bridge.

Doppler effect #2Now we will try the Doppler effect with

both observer and source moving.

ExamplesA car is emitting a sound of 20 hz. If it

is moving towards you at 20 m/s and you are moving away from the source at 10 m/s what is the perceived frequency you hear?

Resonance of open and closed pipesSound can resonate in open and closed

tubes to give us different frequencies for our sound to resonate at.

Much like musical instruments, these frequencies are determined by the length of our tube.

Closed tubesThe sound pressure wave has to have

an area of low and high pressure demonstrated by our anti node. With regular pressure being at the node

See board for node anti node behavior

Open tubesIn an open tube We get an area of high

and low pressure inside our tube but will stay at an even pressure at the ends.

See board for node antinodes behavior

Finding resonant frequencies

ExamplesAn open pipe has a length of 10m.

What is the pipes 1st, 3rd, and fifth, harmonic frequencies?

A closed pipe has a length of 5 m, What is the pipes 1st, 3rd, and fifth, harmonic frequencies?

Physics of musicWe have learned about sound waves,

but today we will learn how to practically apply that knowledge to music

Sound qualityAs you can see our tuning fork creates

a perfect sinusoidal wave. However all fundamental frequencies don’t work like that.

Instruments use the principal of superposition to create pleasant sounding music. The difference between these complex waves is called timbre

String insturmentsUsing what we learned about

fundamental frequencies we can find the fundamental frequencies of guitars, violins, and other string instruments

However, Velocity of our wave is determined by many different things.

Wind instrumentsWind instruments turn vibrations from

your mouth and use resonance to create vibrations which travel through the instrument to produce a larger amplitude.

These instruments use the open and closed pipe ideas except more complex due to the different configurations of your fingers.

ConsonanceWhen two notes are played that sound

pleasant, we call that consonance. Pythagoras experimented with this idea and found the best sounding combonations are in ratios. 1:2, 2:3, 3::4 and so on.

OctavesOctaves are created when two

frequencies are in a 1:2 ratio

For a frequency of 440hz our next higher octave is 880hz.

Another common ratio is 4:5 called the major third