# Experiment utilizing Fourier Analysis

#### cscott

Can anyone help me devise some kind of physics related question (ie. How does resistance varry with area?) involving light or sound where the frequency spectum varries when Fourier Analysis is performed?

Would "How does the frequency spectrum of a light bulb varry with the voltage across it." be valid?

#### berkeman

Mentor
cscott said:
Would "How does the frequency spectrum of a light bulb varry with the voltage across it." be valid?
I guess you could say a few things about the variation of the light spectrum as you took a light bulb from zero volts up to about 150% of its rated voltage. It's mainly hot body radiation variations once the filament starts to glow.

Here are a couple other ideas:

-- Doppler shift of a train whistle as it goes past you

-- Hubble red shift

-- Change in road noise in a car versus speed on various road surfaces

-- Change in the frequency of cars passing by on a freeway versus hour of the day

#### George Jones

Staff Emeritus
Gold Member
How do the Fouier components of a musical note affect the sound of a note?

One of the reasons differenet musical instruments sound different when playing the same (sustained) note is because of the different components present, and and because of different relative strengths of the various components.

Regards,
George

#### cscott

It's been a while, but I've considered all your suggestions!

I guess you could say a few things about the variation of the light spectrum as you took a light bulb from zero volts up to about 150% of its rated voltage. It's mainly hot body radiation variations once the filament starts to glow.
Berkman, can you explain a bit more? Would there be enough change in the spectrum to be worth the experiment as a project? Will only the magnitudes change? What about with light bulb dimmer switches? Or dimmer switches with fluorescent light bulbs?

...would we be able to do anything cool with those hydrogen/helium/etc. lights that will give off the element's nuclear spectrum?

More ideas welcome!

#### cscott

Ouch... we may not be able to get the equipment for working with light. I'll get back to you asap!

#### berkeman

Mentor
cscott said:
Berkman, can you explain a bit more? Would there be enough change in the spectrum to be worth the experiment as a project? Will only the magnitudes change? What about with light bulb dimmer switches? Or dimmer switches with fluorescent light bulbs?
The spectrum of "black body radiation" changes with the temperature of the object:

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#### cscott

George Jones said:
How do the Fouier components of a musical note affect the sound of a note?

One of the reasons differenet musical instruments sound different when playing the same (sustained) note is because of the different components present, and and because of different relative strengths of the various components.

Regards,
George
Due to equipment considerations we've gone to working with sound. My partner and I liked your question George, but we have a few questions:

We have an electric bass and a double bass (acoustic) and we were wondering where the difference in sound would really be coming from between these two intruments. Our FFT graphs show the same obvious spikes (for instance, ~165 Hz when playing E3) but electric still doesn't give the same "sound" as an acoustic.

#### berkeman

Mentor
cscott said:
Our FFT graphs show the same obvious spikes (for instance, ~165 Hz when playing E3) but electric still doesn't give the same "sound" as an acoustic.
What else do you see on the two spectra?

#### cscott

berkeman said:
What else do you see on the two spectra?
First off I should say we're using the FFT in Pasco's Data Studio (they make the equipment that we use to input into the computer, which came from our local university - looks like it'd be first-year lab equipment.) In light of this, we can only get relative amplitudes (I'm guessing you know all this:tongue2:)

Anyway, when playing a note with the electric we can get a quite "flat" line except for the spike at the proper frequency, but "flat" is only relative because the volume of the amp can aid in drowning out any other frequencies or background noise. (So we're micing the amp here - I never thought of inputing directly from the patch cord, but we'll try that next.)

With the stand-up bass it's easy to get a mess all up the range of frequencies along with a notable spike where it should be. However, there are sometimes other notable spikes of amplitude 1.0 which don't really have an explanation. It's hard to tell how much is just background noise or if some of it coming form the intrument itself, even when comparing it to the Fourier spectrum of the ambient noise itself. Lets just say our results so far aren't that consistent with the stand-up.

I'll try to get some of the graphs posted at some point.

#### cscott

I've been trying to brush up on general sound theory to perhaps get some ideas. What about something like the differences in accoustic envelope?

#### berkeman

Mentor
cscott said:
I've been trying to brush up on general sound theory to perhaps get some ideas. What about something like the differences in accoustic envelope?
That's a good item to consider. What would be best would be to calculate the spectra of each instrument as a function of time. That's a different kind of signal processing than just taking the Fourier transform of a long waveform to see it in the frequency domain instead of the time domain. A Fourier Analyzer (I think that's what they are called) analyzes the energy in many sub-spectra bands all at the same time. Kind of like you see with a bar graph display of an audio spectrum -- each one of the bar graphs is basically a narrow bandpass filter of a portion of the spectrum.

BTW, I was googling just now for Fourier Analyzer +"real time", and got some interesting hits. Check out some of this sound/music analysis software:

#### cscott

Well, I downloaded some of that software and created some mp3's of loops from GarageBand. Running a real-time analysis of frequency vs. time, you can very visibly see the difference in how the notes "play out" on the different instruments.

This is going to help us loads, thanks a lot!

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