A line of dancers can dance out the motions of air parcels in a sound wave.
To Do and Notice
Have the dancers stand in a line shoulder to shoulder.
If you have enough dancers make them into pairs of lines facing each other, so dancers in one line can watch the motion of the other line.
Have each dancer put his or her hands on hips and stick out elbows until the dancers are standing with their elbows touching.
This is their rest position, the spacing represents atmospheric pressure.
Have the dancers place a piece of masking tape on the floor between their feet to mark their resting place.
Take a cord and use it to make a half of a sine
wave on the floor in the following way:
The wave starts between the feet of the first dancer on the left.
The wave comes out in front of the dancers reaching a maximum of 1 meter at the middle dancer of the line, dancer #5.
The wave returns to zero between the feet of the last dancer, #9.
The wave represents the fundamental frequency of a tube closed at both ends. The end dancers are up against the wall and cannot move. The wave is shown coming out in front of the dancers, however, it represents motion of the dancers to their right along the line.
Have each dancer cut a piece of string so that it stretches from the tape between their feet to the main cord wave.
Then they take this string and place it on the ground starting at the tape between their feet and pointing to the right.
Have each dancer move to the end of their string.
They have just moved to one position of the air parcels during their motion in the fundamental oscillation of the tube.
Now pull the cord straight.
Every dancer is zero distance from the cord so they all return to their resting position.
Now make the half sine wave behind the dancers. This means that they move the other way, to the left. They will move the same distance to the left as they moved to the right
then go the other way.
What's Going On?
The dancers first bunch together at the right end of the line and spread apart at the left end. When air molecules bunch together there is high pressure. When air molecules move apart there is lower pressure.
Then the dancers bunch together at the left end and spread apart at the right end. Notice that at the ends of the line the pressure goes from high to low and back again. While in the middle the pressure doesn't change.
The ends of the line are places where the dancers do not move, they are nodes of motion.
They are places where the pressure change is
They are antinodes of pressure change.
The center of the line is a place where dancers
move a lot, it is an antinode of motion.
However the dancers stay the same distance apart. It is a node of pressure change.
Now do the dance. Have each dancer remember their home position, their rightmost position and their leftmost position.
Count 1,2,3,4 out loud.
The dancers start at their home positions.
The second harmonic.
Have the dancers return to their rest position.
Now make a wave in string that starts at the feet of the left end dancer, goes in front of the dancers to a maximum amplitude of 1 meter, at dancer #3, then goes to zero at the middle dancer, #5. It then goes behind the dancers to a maximum amplitude of 1 m behind dancer #7 and back to zero again at dancer #9.
Once again have the dancers cut string with a length that reaches from their home tape to the cord.
If the cord is in front of the dancers they move to their right the length of the string. If the line is behind the dancers they move to the left.
Next have them all return to their rest positions.
Then make a wave that starts at dancer #1 and goes behind the line, coming to zero again at the middle then moves in front of the dancers and returning to zero at dancer #9.
Have the dancers move to new positions represented by this line.
Now count the rhythm and do the dance. 1,2,3,4,1,2,3,4.
What's Going On?
There is a node of motion in the middle of this line. Dancer 5 does not move.
There is an antinode of pressure at dancer #5, the dancers alternately spread apart around and crowd together around dancer #5.
When the pressure is high near dancer 1 it is low near dancer 5 and high near dancer 9. The pressures at the nodes alternate along the line.
The fundamental of a tube open at both ends.
Make a sine wave with a zero in the middle at dancer # 5.
The sine wave goes to a maximum of 1 meter in front of the dancers at dancer number 0 and goes to a minimum 1 meter behind dancer number 9.
Once again have the dancers cut string with a length that reaches from their home tape to the line.
If the line is in front of the dancers they move to their right the length of the string. If the line is behind the dancers they move to the left.
Have the dancers move back to their home positions.
Then move the string into a sinewave which starts behind dancer 1, goes to zero at dancer 5 and moves in front of dancer 9.
Count the rhythm and do the dance.
What's Going On?
Here the dancers at the ends of the tube are at antinodes of motion. While the dancer in the middle, #5, is at a node.
The pressure change is greatest at dancer number 5 and is least at the ends of the tube. The ends are at nodes of pressure change the center is an antinode of pressure change.
Return to Day 10
Scientific Explorations with Paul Doherty
25 May 2000