Waves Resource Packet (comments to: moloney@nextwork.rose-hulman.edu)

Suggestions for 'Active' Classroom Learning

While sailing on the Chesapeake bay, a person observed that the sound of a buoy could be heard from a long distance away, while sailing into the wind, and also sailing toward the buoy. But only a short distance after passing the buoy, this person noticed that the sound from the buoy could no longer be heard. He correctly reasoned that the wind speed of 5 knots or less could not be responsible for this effect.

Try to make an argument which will explain this effect, based on the velocity of sound increasing with height above the water. [Hint: you may want to run the windbend.ms file, which shows how wavefronts bend when wind speed changes with height.] Draw some sketches showing how things will be different upwind and downwind of the buoy.

(Good classroom problem after mass-spring behavior is discussed, including energy.)

A proposed automobile design has the bumper effectively attached to the body of an 1100-kg car by a spring of constant 150 N/m. The body structure is capable of withstanding a 5.5g's without suffering damage due to crumpling. The car must pass a 'crash test' at 5 mph with a stationary obstacle.
a) Is this a satisfactory design? State the reasons for your conclusion.
[No, g forces are very low, but bumper length is much too great.]
b) If the design is not satisfactory, improve the design to meet the crash test specs without serious objections to your modified design. [The spring constant can be greatly increased and still meet the spec, with a much shorter length of bumper.]


create a 'slow' timer in a cramped space (after physical pendulum has been discussed)

You need to create a timer which does one cycle in 2.340 seconds. This timer must be operated by gravity and must fit in a shipping container which is 0.21 m x 0.09m x 0.63m. The customer wants this shipped by tomorrow morning via UPS 2-day air. What design will do the trick?? Draw a sketch of your design, and work out the details. Hint: check the problem sketches in the back of Crummett&Western chapter 14.

Background. (After 'beats' are discussed) Radio interference due to accidental beats (mixing of radio signals, related to 'beats', since sum and difference frequencies are created). In an FM radio, the signals are amplified at a frequency of 10.7 Mhz. In order to tune your radio, you adjust a frequency created inside your radio (the local oscillator). This signal mixes with the incoming signal (say, at 100.2 MHz) and the difference of the two signals is formed. When this difference (beat) frequency is equal to 10.7 Mhz, you have 'tuned in' the station, the difference frequency is amplified, and you hear the station's signal.

A destroyer was undergoing refit in the Boston Navy Shipyard. A Boston classical music station was tuned in, at around 103 MHz, but often the music was interrupted briefly by conversations between pilots of aircraft near Logan Airport and the tower. Explain what was causing this effect? Were the aircraft illegally using the commercial range of 88-110 MHz, or was some fundamental physics at work?

The pilots were talking to the tower on a channel around 120 MHz.

The Indianapolis Zoo wants to enhance their aquarium exhibit by using curved glass instead of flat glass. They want to use glass whose radius of curvature is 20 feet, bowing out away from the fish and toward the viewing audience. Without using equations, think about a fish which is located at the center of curvature of the glass.
  Where will its image be located?
  Does this tell you anything about the value using this shape of glass?

[Same spot! No magnification].

{It won't help make the fish look bigger, and it may break. More magnification would be had by bending the glass in toward the fish, and it would stand up better under the stresses from the water in the tank.

Suppose that part of the 24-hour LeMans auto race takes place near sunset at a place bordered by a building with a huge glass front. Drivers are confronted by the setting sun to their left just above the road, and a gigantic glare coming from the right, where sunlight is reflected off the windows of the building next to the road. This causes several drivers to be blinded and crash, even though they were wearing glare-reducing polaroid sunglasses. Your driver wishes to stay alive. Use your knowledge of physics to advise him about surviving this situation using his standard equipment.

[Must rotate his head with glasses on by 90 degrees to block reflected glare from vertical windows!]

In this problem we assume that the opening in a cat's eye behaves like a slit of constant width. Five cats are sitting side by side looking at the headlights of an oncoming car (wavelength = 550 nm). The separation of the car's headlights is 1.90 m and the car is 3600 m from the cats. Each cat has its eye slit adjusted differently while looking at the oncoming car. Here is a table of the cats and their eye widths. From the table, determine which of the cats will be able to resolve the headlights of the oncoming car.

eye          Cat A     Cat B     Cat C     Cat D     Cat E
slit width 2.4 mm   1.9 mm   1.4 mm   0.9 mm   0.4 mm

[Cats A, B, and C can resolve the car headlights].

Early satellite dishes were about 2 meters in diameter, while the newest dishes are as small as 1/2 m in diameter. What does this tell you about the frequencies used in earlier satellites and the newest satellites?

Bring a signal generator to class and a tuning fork. Sound the tuning fork and then have the class select a frequency to play through the speaker. They continue until someone can guess within 1 Hz the frequency of the fork. [They must get close enough to hear beats, then must figure out if the frequency is too high or too low. This might be implemented as a computer exercise, with a 'mystery tone' being sounded, and the user gets 5 tries to select tones then give his best guess as to the value of the unknown tone.]

Reflection of light from an interface near the critical angle can play an important role. The sketch below shows how a modern optical system detects oil or gas at great depth, temperature, and pressure.