12.6. Wave Motion Problem Set http://www.ck12.org
12.6 Wave Motion Problem Set
- A violin string vibrates, when struck, as a standing wave with a frequency of 260 Hz. When you place your
finger on the same string so that its length is reduced to 2/3 of its original length, what is its new vibration
frequency? - The simple bridge shown here oscillated up and down pretty violently four times every second as a result of
an earthquake.
a. What was the frequency of the shaking inHz?
b. Why was the bridge oscillating so violently?
c. Calculate two other frequencies that would be considered “dangerous” for the bridge.
d. What could you do to make the bridge safer?- The speed of water waves in deep oceans is proportional to the wavelength, which is why tsunamis, with their
huge wavelengths, move at incredible speeds. The speed of water waves in shallow water is proportional to
depth, which is why the waves “break” at shore. Draw a sketch which accurately portrays these concepts. - Below you will find actual measurements of acceleration as observed by a seismometer during a relatively
small earthquake. An earthquake can be thought of as a whole bunch of different waves all piled up on top of
each other.
a. Estimate (using a ruler) the approximate period of oscillationTof the minor aftershock which occurs
aroundt=40 sec.
b. Convert your estimated period from part (a) into a frequencyfinHz.
c. Suppose a wave with frequencyffrom part(b)is traveling through concrete as a result of the earthquake.
What is the wavelengthλof that wave in meters? (The speed of sound in concrete is approximately
v=3200 m/s.)- The length of the western section of the Bay Bridge is 2.7 km.
a. Draw a side-view of the western section of the Bay Bridge and identify all the ’nodes’ in the bridge.
b. Assume that the bridge is concrete (the speed of sound in concrete is 3200 m/s). What is the lowest
frequency of vibration for the bridge? (You can assume that the towers are equally spaced, and that the
central support is equidistant from both middle towers. The best way to approach this problem is by
drawing in a wave that “works.”)