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 4.00s 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/s²?  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.