# Sound

Turn in your answers to the following problems below. As always, make sure to show all of your work.

1. Sound waves travel through an aluminum bar at a speed of 1400 m/s. If the frequency of the sound wave is 1000 Hz, what is the distance between crests on a sound wave traveling through aluminum?

2. An airplane flies horizontally at a constant speed, piloted by rescuers who are searching for a disabled boat. When the plane is directly above the boat, the boat’s crew blows a loud horn. By the time plane’s sound detector receives the horn’s sound, the plane has traveled a distance equal to one-half its altitude above the ocean. (The speed of sound is 343 m/s.) If it takes the sound **4.00**s to reach the plane, determine

a) the altitude of the plane, and

b) its speed, in m/s. What is its speed in knots (nautical miles per hour)?

3. (Rev 9/11) Estimate the wavelength of a 20,000 Hz sound wave, which is near the upper limit of audibility for humans. Assume air at standard temperature and pressure.

4)(9/11) An organ pipe is a closed-ended air column. If its bottom note has a frequency of 20 Hz (close to the lowest audible frequency), then how long is the column? Assume standard temperature and pressure.

5. (Rev 2/11) The sound of a truck horn, observed when the truck is stationary, is 440 Hz. A drunk is sitting in the middle of the road at night. He sees the truck’s headlights, and hears a 480 Hz horn. How rapidly is the truck approaching him, in m/s^{2}? In mph? (As before, assume the speed of sound in air is 343 m/s.)

## Case Assignment Expectations:

In general, Cases are expected to possess the attributes of precision, clarity, breadth, depth, and critical thinking. *Not all* of these are relevant to the answer to *every* problem in the case. When it *is* relevant, the evidence for each attribute is as follows.

- Precision: Numerical answers are calculated correctly, to the correct number of significant figures.
- Clarity: The problem is restated in its simplest form. Relevant variables are identified. Formulas are algebraically rearranged, as necessary. All the mathematical steps are shown, in logical order.
- Breadth: Where discussion is required, the question is placed in context. Alternatives are considered.
- Depth: Where discussion is required, the question is examined in detail. No relevant aspect of the question is omitted.
- Critical thinking: The correct analytical approach is selected. Relevant data areidentified and irrelevant data are ignored. When required, the practical importance of the principle or phenomenon is accurately described.