Physics A: Problem Set 10: The nature of waves

types of waves

1. A freight train at rest starts moving forward. There is enough slack in the couplings between cars that, after the first car starts moving, there is a slight delay before the second car starts to move. Then, after the second car starts moving, there is a slight delay before the third car starts to move. Likewise, after the third car starts moving (keep repeating this procedure over and over again) until finally the last car starts to move. This phenomenon satisfies the definition of a wave. Is the wave I just described a…
   1. mechanical or electromagnetic wave?
   2. transverse, longitudinal, complex, or torsional wave?
   3. pulse or a periodic wave?
   4. standing or traveling wave?

periodic waves

2. The graph below is a record of sea level heights recorded at Hanimaadhoo, Maldives during the tsunami of 26 December 2004. The data were filtered to eliminate the normal tidal fluctuations, so what you are seeing is the increase in sea level due to the tsunami. (Data source: University of Hawaii Sea Level Center)

   

   Natural phenomena are normally noisy (in the statistical sense) but from 10:50 to 12:05 local time the changes in sea level at Hanimaadhoo were most nearly periodic. During this time interval determine the tsunami's mean…
   1. amplitude
   2. period
   The speed of a tsunami varies with depth. In the open ocean they normally move as fast as a commercial jet airplane (about 250 m/s or 900 kph) but slow down to the speed of a car on a neighborhood street when they reach the shallow waters of the shore (about 15 m/s or 55 kph). Given these speeds, determine the mean wavelength of the segment of the tsunami that arrived in Hanimaadhoo between 10:50 and 12:05 when they were…
   3. in deep water
   4. near the shore
   One final question.
   5. How would the amplitude of a tsunami near shore compare to the amplitude of the same wave in the open ocean? Explain your reasoning.
3. Each of the six strings on an acoustic guitar is 80 cm long and generates a wave that's twice the length of the string when picked or strummed. Determine the wave speed of each string given the following tuning.
   5. 082.41 Hz
   1. 110.00 Hz
   4. 146.83 Hz
   7. 196.00 Hz
   2. 246.94 Hz
   5. 329.63 Hz
4. A viola string is 36 cm long and plays a certain note when the finger is not resting on the string. How far from the bridge should a finger be placed so as to produce a note that is…
   1. an octave higher (double the original frequency)?
   2. two octaves higher (quadruple the original frequency)?
   3. a fifth higher (³₂ the original frequency)?
   4. a fourth higher (⁴₃ the original frequency)?