Investigation 8
Vibrations and Waves
Part I - Mass oscillating on a spring.
1. Does the amplitude of the oscillations affect the frequency of a mass oscillating on a spring? If so, then how is the frequency related to the amplitude?
What do you think?
2. Does the amount of mass attached to the spring affect the frequency of oscillation? If so, then how is the frequency related to the mass?
What do you think?
You will need: a ring stand, a pendulum clamp, a spring, a weight hanger, three 200 gram masses, and a stopwatch.
Amplitude changes:
Set up your experimental system according to the diagram to the right. Be sure to add 200 grams to the weight hanger.
Set the hanging mass oscillating with a small amplitude. Measure the time for 10 complete oscillations. Record the value in the table below. Repeat the small amplitude oscillations two more times and record. Calculate the average time for 10 oscillations, then the period of the oscillation, and then the frequency of the oscillation.
Repeat the above instructions for medium amplitude oscillations.
Repeat again for larger amplitude oscillations.
Amplitude / Time for 10 Oscillations (sec) / Average(sec) / Period
(sec) / Frequency
(Hz)
1st trial / 2nd trial / 3rd trial
small
medium
larger
From the experiment you performed above, is there definitive evidence that shows how the amplitude of the oscillation is related to the frequency? Explain.
Mass changes:
See whether or not changing the mass that is oscillating changes the frequency.
Set the spring system oscillating with 200 grams on the weight hanger and time 10 oscillations. Repeat this two more times. Calculate the average time for 10 oscillations, then the period of the oscillation, and then the frequency of the oscillation. Now add another 200 grams to the weight hanger (400 g total) and repeat your three trials for 10 oscillations. Repeat again with another 200 g added (600 g total).
Mass on Weight Hanger / Time for 10 Oscillations (sec) / Average(sec) / Period
(sec) / Frequency
(Hz)
1st trial / 2nd trial / 3rd trial
200 g
400 g
600g
From the experiment you performed above, is there definitive evidence that shows how the mass that is oscillating is related to the frequency of oscillation? Explain why what you observed occurred.
Part II – The simple pendulum.
1. For a simple pendulum with a fixed length, does the mass affect the period of oscillation? That is, does a heavier mass increase, decrease, or not affect the period?
What do you think?
2. Does the length of the simple pendulum affect its period? That is, by making the length of the pendulum shorter does the period increase, decrease, or remain the same?
What do you think?
In addition to the supplies you already have, you will need two pendulum balls with differing mass and some string.
Mass changes:
Set up your experimental system according to the diagram on the right. Use one pendulum mass. When the length of the pendulum is measured, measure from the center of the mass to the point where the string is clamped onto the pendulum clamp. In order to change the length of the pendulum, simply loosen the screw and slide the string up or down to shorten or lengthen the string.
Adjust the length of the string until the simple pendulum length is 50 cm. Measure the time for 10 oscillations and record. Repeat this measurement two more times. Calculate the average time for 10 oscillations, then the period of the oscillation, and then the frequency of the oscillation. Add an additional mass and measure the time for 10 oscillations. Add another mass and repeat the measurements.
Pendulum Mass / Time for 10 Oscillations (sec) / Average(sec) / Period
(sec) / Frequency
(Hz)
1st trial / 2nd trial / 3rd trial
100 g
200 g
300g
Do your results show that there is a relationship between the oscillating mass and the frequency of oscillation of the pendulum? Explain.
Length changes:
We will now determine how the length of a simple pendulum might affect the frequency of oscillation of a pendulum. Use one mass and adjust the length of the pendulum to be 100 cm. (Be very careful making this measurement.) Now time 10 complete oscillations and record. Repeat the measurement two more times to ensure you made the measurement correctly. Calculate the average time for 10 oscillations, then the period of the oscillation, and then the frequency of the oscillation.
Adjust the length of the pendulum to 40 cm and repeat your measurements. Then do it again for 10 and record your data in the table and find the frequency for each of the lengths.
Length of Pendulum / Time for 10 Oscillations (sec) / Average(sec) / Period
(sec) / Frequency
(Hz)
1st trial / 2nd trial / 3rd trial
100 cm
40 cm
10 cm
Do your results show that there is a relationship between the length of the pendulum and the frequency of oscillation of the pendulum? Explain.
Part III - Waves
1. A string is attached to a mass that is oscillating up and down in simple harmonic motion. The frequency of oscillation of the mass is 4 Hz. This oscillation produces a harmonic wave traveling to the right on the string, as shown.
Use a ruler and measure the wavelength and amplitude of the wave:
a. Wavelength = _____6.1______cm
b. Amplitude = ______1.5______cm
c. How fast is the wave moving to the right?
SPEED OF WAVE = FREQUENCY x WAVELENGTH = (4 HZ) x (6.1 CM) = 24.4 CM/SEC
d. If the tension in the string is increased, will the waves travel faster, slower, or continue at their original speed? (Do you know why? Tough question – you don’t need to write an answer. Just think about a short segment of string at the crest of the wave and how the forces that are pulling on it change.)
FASTER – THE FORCE PULLING UP AND DOWN ON THE STRING WILL BE GREATER CAUSING THE STRING TO HAVE A GREATER UP AND DOWN ACCELERATION.
e. If the mass of the string is increased, will the waves travel faster, slower, or continue at their original speed? (Do you know why?)
SLOWER – MORE MASS MEANS MORE INERTIA (RESISTANCE TO CHANGE)
2. A physics student watches the ocean waves approach and pass the end of Santa Monica pier. She notices that the crests are 15 meters apart. She also notices some debris in the water and observes its motion.
a. Describe the motion of the debris as the water wave passes it.
THE MOTION IS A COMBINATION OF UP AND DOWN AND BACK AND FORTH – KIND OF A CIRCULAR PATH
b. She also notices that starting from the time a crest reaches the end of the pier, the time it takes the next crest to reach the end of the pier is 5 seconds.
What is the period of the wave?
PERIOD = T = 5 SECONDS
What is the speed of the wave?
SPEED = FREQUENCY x WAVELENGTH = (1/PERIOD) x WAVELENGTH = (1/5) x 15 M
= 3 M/S