High School Mathematics-Physics SMILE Meeting 1997-2006 Academic Years Waves

25 November 1997: Bill Blunk [Joliet Central HS]
A Simple demo of wave beats using pop bottles.

Having the bottles filled more than half and blowing over the tops produces a tone, the frequency of which can be changed by adding or subtracting some of the H₂O in the bottles. One person can excite the two bottles, but it is much more practical for two people, each with one bottle.

Comments were made that an echo at a time of about 40milliseconds [ms] later is acceptable, whereas echoes at time delays of 200 ms are aesthetically detrimental. A live room with a short echo is appreciated while echoes over time intervals greater than 100 ms cause the sounds to seem dissonant to the listener. Also, piano tuners use harmonic resonance to tune a piano in the higher octaves, [ http://hyperphysics.phy-astr.gsu.edu/hbase/music/pianof.html#c1] and they can resolve differences of 1/5 cps using beats.

01 May 2001 Fred Farnell (Lane Tech HS, Physics)  What happens when waves meet?
put some paper cups on the floor and stretched a slinky™ across the floor, which was held at its ends by two assistants.  An assistant, by rapidly moving his end of the spring back and forth once {transverse to the direction of the stretched string), sends a transverse wave pulse toward the other end. When the other end was held fixed, the wave was seen to reverse its orientation and direction after reflection at the fixed end.  The cups were put parallel to the stretched slinky on both sides of it, and the goal was to set up waves that would knock down all of the cups.  This was seen to be difficult, if not impossible.  Then, the assistants set up waves coming in simultaneously from each end, so that we could see the slinky before, during, and after the overlapping intersection of the wave pulses in the middle.  Very interesting, Fred!

22 April 2003: Ann Brandon [Joliet West HS, Physics]      Waves and Resonance
Ann led us through three exercises to illustrate wave properties:

• First she took an ordinary tuning fork [marked 512 Hz --- nominal frequency of High C], struck it against a large, hard rubber stopper to produce vibration, and held it vertically by its shaft at a distance of 15-30 cm from her ear. Ann then slowly rotated the shaft about a vertical axis, and slowly moved it around. She listened carefully, and said that she was able to identify locations of minimum and maximum sound intensity, which were produced by interference of the sound coming from two sides (tines) of the tuning fork. Ann said that any tuning fork within the range of normal hearing would work very well for this exercise, which could be made quantitative in a laboratory experiment. We passed the tuning fork around the class, and each of us listened to our heart's content!
• Next she took out a Sonalert Device [which produces penetrating sound at high pitch], which is very similar to a device available at modest cost at Radio Shack. It was attached to a small battery pack to form a compact module. That module had been securely taped together with electrical tape, with a bright orange cord firmly attached. Ann rotated the module around her head in a horizontal circle of radius about 1 meter, by tightly holding the other end of the cord, and swinging it slingshot style, as in the Biblical account of David and Goliath. We could plainly hear the changes in pitch, corresponding to lower frequency when the module was moving away from us, and higher frequency when it was coming toward us.  A superb illustration of the Doppler Shift, for everybody to see and hear! For more details see the UCB Physics Lecture Demonstration website: [ http://www.mip.berkeley.edu/physics/B+65+0.html].
• Home-made Resonance Maker:  Ann showed us her home-made apparatus to show transverse oscillations of a vibrating cord, which had been designed and constructed as a shop project in the Summer SMILE program several years ago. The apparatus --- for which the materials cost less than $10 --- consists of a plywood platform [about 30 ´ 50 cm], two pieces of plastic pipe, four elbow joints, 2 DC motors [0-3 V, available at American Science Center or Radio Shack], and some sturdy cord. The pipes are attached to the platform at opposite (longer) ends with wrapping metal supports, with elbow joints at both ends --- at the bottom to attach the pipe to the platform, permitting rotation, and at the top for attaching the motors. A cord is tied between the motors, and the motors set up (small) transverse motions at each end of the cord, as shown: A transverse standing wave is set up on the vibrating cord.  The tension in the cord is varied by adjusting the orientation of the two plastic pipes.  By appropriate adjustment, we are able to produce standing wave patterns on the cord.  How come? The standing wave patterns (fixed ends) occur whenever L = n l / 2, where L is the (fixed) length of the cord, l is the wavelength, and n is the order of the resonance.  The speed of longitudinal vibrations of the cord is given by v = l f = (2 L/n) f = Ö [T / m ],  where the mass per unit length of the cord is m.  By decreasing the tension T, we thus decrease the velocity v. Since the motors vibrate at a steady rate, f, the frequency of vibration of the cord remains fixed, whereas the wavelength l decreases. Since the length of the cord remains fixed, we should be able to fit more standing waves on the cord by reducing the tension.  That is exactly what we observed! Amazing!

Don Kanner [Lane Tech HS,  Physics]           A Quick Connection 
Don  was inspired to think about Physics when he saw a girl with a pony tail hairdo running into the wind and away from him.  The girl's ponytail moved in a circular pattern on the left side, and then swished to the right side to move in a circular pattern there.  Why didn't rotate up and down, instead? Don felt that the eddies in the wind produced this "resonant oscillation", similarly to those in the collapse of the Tacoma Narrows Bridge in November 1940 (see the SMILE writeup for 25 February 2003: mp022503.html).  Don felt that "somebody" should obtain a DVD recorder and make digital images to illustrate various principles and concepts of physics.  Is this practical?

Thanks, Don.

12 April 2005: Ann Brandon [Joliet West HS, physics]              Making Waves
Ann showed us her home-made device for showing modes of vibration of a string.  The device contains a dry cell battery pack, two DC motors, a potentiometer, string, and two plastic rods attached to a wooden base.  The motors are anchored to the plastic rods and attached to drive opposite ends of the string..  Transverse vibrations of the string are induced, with the tension in the string varied by stretching it. For details and a photo see the notes from the Math-Physics SMILE meeting of 22 April 2003:  mp042203.html. As the tension in the string is increased, the velocity v of transverse vibrations also increases.  The frequency f of transverse vibrations is determined by the (fixed) rotational frequency of the motors.  Because of the relation v = l f, the wavelength l increases in this case. We thus get fewer nodes on the string when we increase the tension. We produced stable oscillations with 1, 2, 3, and 4 internal nodes on the string.

Ann will bring materials for us to construct several of the devices at our next meeting,.  Great physics show! Thanks, Ann.

26 April 2005: Ann Brandon [Joliet West HS, physics]              Workshop on Standing Wave Machine
Ann held a workshop in which 8 participants constructed the standing wave machine, which she showed us at the last SMILE meeting, mp041205.html.  Good job, everybody! Special thanks to Ann.