Message-Id: <l03102801b150ac1f6719@[209.142.17.104]>
In-Reply-To: <n1322029439.8264a@Tesla.exploratorium.edu>
Date: Tue, 7 Apr 1998 23:22:45 -0700
To: "Pinhole Listserv" <pinhole@exploratorium.edu>
From: Ron Wong <ronwong@inreach.com>
Subject: Re: diffraction of sound
A while ago, Geoff Ruth said:
>A student of mine had the following question in class on Friday:
>
>If someone is standing around a corner from you, how can you hear them? His
>answer was that the sound waves bent as they went around the corner.
>>........Then he asked this: if you were in the desert with nothing around,
>and you stood around a corner from someone, could you hear them talking?
>.........Is there any amount of diffraction that happens as sound waves go
>around corners?
Any wave phenomena will, under the right circumstances, exhibit diffraction
whether it be x-rays, light, radar, water waves, or sound.
Huygen's Principle, as stated by Al Sefl, that "each point of a wave front
may be regarded as a new source of disturbance" is a fine way to explain
the phenomena to your students but be aware that, although sufficient, it
is only a beginning.
It works very well in explaining the propagation of a straight wave. Here
the circular waves created by the infinite number of point souces along a
given wave front meet at any given time in such a way that the crests and
troughs produce the next succeding straight wave in the direction of
propagation. For the wave front to remain straight, each point on the wave
front must "see" an infinite number of points on each side generating their
individual circular waves.
If a straight wave is moving parallel to a wall then the wall acts like a
mirror and the point of the wave front next to the wall "sees" an infinite
line of point sources extending off in the direction of the wall. The
result is that the straight wave remains straight. When it gets to the end
of the wall (the corner referred to by the student) then the image of the
straight wave disappears and there is nolonger an image of a line of point
sources of circular waves in the region that was once occupied by the wall.
The result is that the circular waves created by the points that were next
to the wall just as the wave reached the corner no longer interfere with
one another in a manner that would maintain a straight wave in the area
immediately around and beyond the corner. Since these points were creating
circular waves at the time, we see the result of their interference with
one another - a circular wave front radiating out into the region around
the corner.
Some version of the above explanation would probably satisfy the curiosity
of most students and may be sufficient for your needs. But it isn't
complete.
The Exploratorium once had a series of ripple tanks hidden away in some
obscure place in the museum that brought out some of the more subtler but
very important aspects of diffraction using water waves. I haven't seen it
lately but you can probably cobble together a ripple tank of your own to
demonstrate to your student/class that the answer to his question is
"maybe".
The amount of diffraction depends on wavelength.
This is very easy to demonstrate with a ripple tank.
Place a barrier in front of a straight wave and you'll be able to show that
large wavelengths produce significant diffraction and that small
wavelengths produce negligible/no diffraction.
Create an opening by placing two barriers close to one another. When the
opening is large compared to the wavelengths the diffraction is
small/negligible. On the other hand, when the opening is small the
diffraction is large and very noticeable (albeit at reduced amplitude).
If you place your ripple tank over an overhead project and move the lens
assembly to the highest position to enhance the shadows of the waves cast
on the screen, you can demonstrate all of this and much more to your entire
class.
To answer your student's question: If he stands around the corner and up
against the wall, he might not hear his friend talking. This is especially
true if he is some distance from the corner. On the other hand, if he
stands the right distance from the wall while just around the corner from
his friend he should be able to pick up his friend's voice. If he listens
carefully, he may notice a change in the quality of his friend's voice.
The higher frequencies will appear to be missing or muted.
Its this dependency between wavelength and diffraction that allows sounds
from the hallway to pass through a door and fill the classroom with sound
(even in the absence of reflection) while the hall light (whose wavelengths
are a millionth of that of sound) will simply cast a sharp silhouette on
the floor/walls (although there were more compelling reasons for objecting
to the wave theory of light this was one of the reasons offered to prove
that light wasn't a wave phenomena - it traveled in straight lines).
One last comment. If, when you are using the ripple tank, the lighting is
just right, your students are really alert and/or you are just plain lucky
you'll see more than just diffraction in the region behind the barrier.
You'll see interference as well. Explaining this takes a little more than
Huygen's Principle but I think I've already taken up enough bandwidth.
ron