# Intensity and Relative Amplitude

#### yahooid2

How would you calculate the intensity using relative amplitude.

Say for a violin...how would you calculate it's intensity for one of it's harmonics or overtones.

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#### jono

What dou you mean by "relative amplitude"?

I hope this doesn't turn into a fourier discussion..

Jonathan

#### yahooid2

like say in a wave...a musical note will create a similar frequency in different instruments, but the relative amplitude differs from instrument to instrument creating a different timbre or tone.

#### jcsd

Gold Member
The tonal qualties of differnt instrumnets come from the different shapes of their waveforms not from their amplitudes (the amplitude of a note is merely a measure of it's volume).

#### chroot

Staff Emeritus
Gold Member
To add to what jcsd said, the timbre of an instrument is defined by its "spectral content."

Think about this: a very boring instrument might play a single, pure sine wave of one frequency. The sound is bland and featureless, and won't impress most audiences.

Now add a little second harmonic -- in other words, if the basic note is middle C, add a little of the C one octave up. Be careful not to add too much -- the middle C should still be the loudest component. This new sound is a little more pleasing -- you can still tell it's a middle C, since the component with the largest amplitude is middle C -- but now the sound has a different timbre.

Real musical instruments have spectral content all over the place -- mostly in harmonics. The loudest note is called the fundamental, and notes of twice, three times, and four times that frequency are called the second, third, and fourth harmonics, and so on. Real instruments' sounds are defined by the amplitudes of all those harmonics -- they're often called "overtones" by musicians. That's why a saxophone and a piano sound very different, even when they both play middle C.

- Warren

#### chroot

Staff Emeritus
Gold Member
And to answer your question, I'm not sure there's really any way to calculate the harmonic content of a violin, for example -- it's a complicated system. The shape of the resonant cavity, the vents, the bridge, etc. all come into play. You might be able to get a first approximation by just analyzing the resonance of a simple cavity, but it won't capture all the complexity that makes a real violin sound so nice.

- Warren

#### turin

Homework Helper
A pure sinusoid sounds cool, kind of eerie.

The fundamental does NOT have to be the loudest, just the lowest.

The spectrum of a piano is nonlinear (meaning Fourier analysis doesn't work well to describe the timbre).

The most important feature of a violin that causes the spectrum is the bow. The wave is predominantly sawtooth, and it doesn't require a terribly faithful reconstruction to simulate. The sawtooth is caused by the bow grabbing the string, pulling it, and then letting go sharply.

Staff Emeritus
Gold Member

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