# SEx Education: The Royal Philharmonic Orchestra Goes to the Bathroom

 SEx
 Science Explained

#### The Royal Philharmonic Orchestra Goes to the Bathroom1

I worry about the SExperts sometimes... Who knows what Guru Roghan Josh was thinking when this popped

Toilets flush in E-flat - everyone knows that. But how do we know
that? Is it a case of someone with perfect pitch telling us, someone
playing notes on a keyboard until it sounds 'right', or is there a
scientific device that can recognise notes?

As seems to be par for the course around here, there's what seems
to be a simple answer to this question, which soon gets lost in the
midst of a heated debate. So before we get lost in the subtleties of
toilet bowl shape and lid position, let's allow Mu
Beta
and Varindweion to deal with
the easy bit:

It's all a case of frequency. Middle C has a frequency of 256Hz,
and it's a simple job for a computer to analyse the strongest
frequencies in any 'white' noise

- Mu Beta
I think you can even use a guitar tuner. If you use a so=called
'chromatic' tuner, it gets real easy: they display the note you are
hitting and how far off you are. So, if you put this next to a toilet
or whatever you want to determine the frequency of, it will display
the note nearest to the measure frequency. For the flush it would
display 'E' and the pointer-thingy would be all the way to the
left2. This
corresponds to a frequency of about 311 Hz

-Varindweion

So far so good. But...

#### 'I'm Not Sure I Buy This'

Seth of Rabi wasn't convinced. Not by
the idea that you can identify the note of a toilet flush, but by the
idea that the note in question was E-flat. Never one to shy away from
a bit of maths, Seth provided this calculation:

A toilet is basically an open pipe with a fundamental frequency
f=v/2L, where v is the speed of sound in air (344m/s at 20°C), and
L is the length of the pipe (water surface to top of pan say ~16" or
0.406m). This gives a frequency of around 423.6Hz or a sharpish
A-flat. To get down to 311Hz the pan would need to be 0.553m (21.8")
deep.

While Seth's calculations were undoubtedly correct, DaveBlackeye wondered if they were strictly
relevant to a toilet bowl.

That would certainly apply if we were using a toilet pan as an
organ pipe. But in fact we are dumping a load of water into it in a
very turbulent fashion. The water behaves chaotically and produces
sound over a wide range of (essentially random) frequencies. The sound
of that water is therefore more like white noise than pink3. If you put it through a rectum
paralyser4 you would see a nice plump plateau rather than
a pronounced spike with harmonics.

Seth agreed that the water behaves chaotically, but noted that this
was similar to, if less focussed than, the behaviour of the lips and
reeds of wind instrument players:

The bowl is still a resonant cavity, with a characteristic
fundamental frequency formed from the standing half-wave equal in
length to the length of the cavity. The bowl shape, just like the bell
of a wind instrument, does not alter the pitch of the fundamental, but
amplifies the sound overall while selectively boosting particular
harmonics.

Dave wasn't quite convinced:

[The shape of the bowl] would appear to be more akin to a
reflecting parabola than a resonant cavity (ie, it would certainly
direct sound upwards out of the bowl but would not change the 'colour'
of the sound by very much)

The question of bowl shape is, of course, further complicated by
whether the last person to use the toilet in question was male or
female...

#### Leaving the Lid Up

Any good experiment should be repeatable, but to achieve this, you
have to know the precise conditions of the original. This got Seth
wondering:

They don't say whether the seat was up or down, do they? Down would
halve the frequency of the fundamental and cut out the even harmonics.
Now, the third harmonic wouldn't be far off E-flat...

Dave concurred, noting that:

With the lid down, higher frequencies are lost in preference to
lower, again shifting the overall bias towards the lower
end5

The debate then moved on to the even more subtle effects of water
temperature on the note and, as I write this, the SExpert jury is
still out. As soon as Dave has had time to grab a rectum paralyser and
find out whether the toilet a) has a definite note and b) whether that
note is E-flat, we'll let you know. Watch this space...

#### QED

This article was based on a conversation at the SEx forum - where science is explained.

Why not pop over with your own questions? The pick of the bunch
will feature in The Post's next
issue.

SEx Education Archive
Archive

Danny B.

08.03.07 Front Page

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1It's an obscure Monty
Python
that...
2This depends on brand and type.3If
you want to more about white and pink noise, try Dr. Hell's Entry on The