How to measure speed of sound in toilet! (or, not to)

It occurred to me that science can happen any time, anywhere. Before we got ready for a jog yesterday, my friend and I made a few funny sounds in our changing room a.k.a the glorious toilets. Suddenly the sound got louder than expected, it amplified in some sort of ways.

Curious enough, we were thinking all the possibilities. Somebody playing a prank in the next cubicle? Or we stumbled upon the dark secret of the toilet? Or it is because of science? Our best educated guess led us to standing wave – our sound waves travelled between the two walls of the toilet cubicle, forming loud and quiet regions along the way.

standing_wave_2
Red & Blue: waves. Black: wave+wave.

Of course, an answer often leads to more questions: what can we do with it? It happens that the width of the wall is related to the speed of sound and the pitch of my voice.

Sketches - 5.png
Simple & crude.

If I know my pitch and the width of the wall, I can measure the speed of sound! With this realisation, I readily set out to a new challenge:

Width

It was measured to be 70cm.

Pitch

I did a recording of my sound in the toilet (for science!):

sound_time
My sound.

You might hear the sound gets louder as the pitch goes lower.

To find out what the dominant frequencies are, I did a voodoo on the sound file (essentially performing a Fast Fourier Transform) using R.

 

In the last image, you can see the dominant frequencies peak at ~115Hz. That gives me a value for speed of sound : 161 metres per second. Which is half of the expected answer (340 metres per second). What a bummer :/

Lesson learnt:

  1. As the sound propagates in three dimensional space, the formula I used is not suitable (2D case only).
  2. I didn’t consider the sound might form standing wave with the floor and the open ceiling as well. All sorts of weird interactions (diffraction, interference etc) were not included.
  3. My voice was far from perfect and produced pitches of different magnitudes which complicates the issue.
  4. Science can be observed everywhere if you look hard enough. Just make sure to grab a friend with you. Silly things are better with friends. 😉

 

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