The Physics
Opus in profectus

Periodic Waves

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  1. 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)

    Line graph

    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…
    1. in deep water
    2. near the shore
    One final question.
    1. How would the amplitude of a tsunami near shore compare to the amplitude of the same wave in the open ocean? Explain your reasoning.
  2. 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.
    1. 082.41 Hz
    2. 110.00 Hz
    3. 146.83 Hz
    4. 196.00 Hz
    5. 246.94 Hz
    6. 329.63 Hz
  3. A viola string is 36 cm long and plays a certain note when the finger is not resting on the string. Where should the 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)?
  4. tsunamis.txt
    The greatest recorded earthquake (magnitude of 9.5) occurred on 22 May 1960 in Chile. The second largest earthquake (magnitude 9.2) occurred on 27 March 1964 during the Christian Holiday of Good Friday, which is why it is also known as the Good Friday Earthquake. A large earthquake (magnitude 8.8) occurred in Chile on 27 February 2010 that grabbed my attention and motivated me to write this problem. All three earthquakes generated tsunamis for which I was able to find useful data.

    Tsunamis are sometimes called "tidal waves" but this name is misleading. Tsunamis, which are seismic in origin, and tides, which are caused by the gravitational pull of the Moon and Sun, are completely unrelated. The word tsunami is derived from the Japanese phrase "harbor wave" (津波) since tsunamis are most intense in harbors where the underlying terrain focuses their energy. The term "tidal wave" is somewhat appropriate since the waves generated by earthquakes result in long period waves that sometimes look like the changes in water depth caused by the tides.

    The accompanying tab-delimited text file provides the following data for the tsunamis associated with the three earthquakes described above. (Data source: National Centers for Environmental Information)

    1. Location of town, harbor, or facility
    2. Region (state, province, or country)
    3. Transit time in minutes after the earthquake began
    4. Distance from the epicenter in kilometers measured along a great circle (the shortest path on the surface of a sphere)

    Use this information to determine the speed of a tsunami in…

    1. km/min
    2. km/hr
    3. m/s
    4. and mph if you live in the United States


  1. problem