S302, Kewley-Port 9/2/07

Homework 2
Vibration and Waves

1. A pressure is measured as 500 dynes/cm2 . What is the equivalent in pascals (use the units PA)?

2. A pendulum is in motion with mass = 2 kg.
a) at the zero displacement (equilibrium), the velocity is .75 m/s. What is the momentum (careful of units) ?_________
b) at the maximum displacement, the momentum is: ____________  Explain

3. You have a geode hanging on the end of a spring system that is vibrating at 2 cycles/sec.
a) Draw a picture of this system, indicating the minimum and maximum points of displacement in the right margin.
b) Draw an arrow and label it to indicate where KE is maximum.
c) Draw an arrow and label it to indicate where PE is maximum.
d) What is its frequency?  _______________

4. Calculate the frequency in Hz of a vibrating system with the period:
a) 4 s

b) 0.5 s

c) .01 s

d) Can you name something that is capable of vibrating with the rate you
calculated in (c)? _________________

5. There is a giant pendulum that is L = 3 meters in length that is in vibration.
a) What is the period of one cycle in seconds?

b) What is the relationship between frequency and the period of the pendulum's vibration?

c) What is the equation of the frequency of vibration using the variables L and G (gravity)?

6.  There are primarily two types of wave motion, transverse and longitudinal. For each type, give a specific example of a physical object that can assume that wave motion, and describe and/or draw the observed waves for that example.

7.    a) What is the speed of sound for a 1000 Hz tone at sealevel?_____________

b) What is the speed of sound for a 3000 Hz tone at sealevel?____________

c) What is the relationship between frequency and the speed of sound?

d) Name three physical properties that do affect the speed of sound, and describe how the speed of sound changes with changes in the property (i.e. does the speed increase or decrease).

8. The following web page shows a longitudinal wave (you’ll need a Javaenabled machine to see it):

http://www.surendranath.org/Applets/Waves/Lwave01/Lwave01Applet.html

The drop-down menus should be set to Progressive Wave, High amplitude, and Low frequency.

Observe the motion of the wave (by watching a bunched-up region of lines) as well as the motion of the individual particles (the individual lines).
On graph paper, draw the waveform corresponding to this longitudinal wave by plotting the displacement of just one of the lines as a function of time.

9. Now I’ve frozen the longitudinal wave in time:

On graph paper, plot the density (crowdedness) of the lines as a function of distance.