# Measuring the period of SHM using sound

1. Dec 31, 2016

### Seanywil

Hello! First time posting here. I'm studying the IB and need to complete my required experimental write-up.
I am looking to replicate the well-known experiment that finds the value of g by investigating the relationship between period and length of string for a simple pendulum.

1. The problem statement, all variables and given/known data

I am required to put a "twist" on my experiment in order to surprise the examiner by my understanding of physics. I have an idea, but cannot find relevant information on the internet about whether it will work.

2. Relevant equations
I will be using the length-period equation of a simple pendulum: T = 2pi sqrt(l/g).

3. The attempt at a solution
My idea is to measure the period of the motion more accurately using digital means, rather than the traditional stopwatch. To my understanding this should provide me with a lower absolute uncertainty.

I seek to measure the period by having a constant sound-producing source as the fixed mass on the pendulum and placing a microphone underneath the middle of the SHM (where the object's speed is greatest). I then want to somehow map the change in frequency (according to the Doppler effect) digitally and measure the time difference between each second maximum frequency to determine the period.

I have a few questions:
1) What sort of software is available for this?
2) Is my experimental setup too dodgy? Will it impair the accuracy of my measurements?
--- (My pendulum is two chairs and a broom between them as the experiment will be done at home)

3) Should I take the average of 10 periods, or just the first one? And why?

4) Any further comments on what I should do, and if this will even work will be appreciated. :)

Thanks a lot!

2. Dec 31, 2016

### Cutter Ketch

I was with you until you said "two chairs and a broom". That kind of put a scale on the sophistication of the experiment for me. It will be tough to measure anything brilliantly accurately with that quality of equipment, but I suppose you work with what you have.

As for coming up with something original to surprise the examiner, I love your idea of using a source on the pendulum and using the Doppler shift. I am sure that is exactly the sort of out of the box clever twist that would please him. Unfortunately I'm not sure it wil work. The Doppler shift depends on the speed compared to the speed of sound. Your pendulum will not be moving even 1% of the speed of sound, so you would need to measure Doppler shifts in the single Hz range. The fundamental problem with that is it takes a full second of listening to see that the frequency has changed by 1 Hz. Not good for timing.

You could have a quiet source pass close to the microphone and note the peak of the amplitude.

Of course the less clever but more usual approach is a laser and a light sensor. Then you time when the light interrupts the beam.

Regarding software for analyzing sound, it sounds like you are on a shoe string budget, so what might be free? If you or anyone you know has a Mac, they come with Garage Band which lets you record a track and then look at the time plot. That would be perfect for the amplitude measurement I suggested.

Other general comments: for accuracy you will want the bob to be much heavier than the string, and keep the arc of the swing short so that the small angle approximation is very good.