Introduction to Vibration and Waves I v06a
Spring Scale (5 N capacity)
In this lab we will use very simple apparatus to qualitatively and quantitatively explore several aspects of the properties of vibrations and waves. First we will explore the oscillatory motion exhibited by a pendulum. Next we will observe two different types of waves and arrive at a definition of a wave. Next, we will make determinations of the speed of the wave on a slinky and observe the dependence of the wave speed on the mass density and the tension of the slinky.
Part 1: Types of Waves and the Definition of a Wave
Stretch the slinky a distance of several meters on the floor. Shake the slinky sharply to the right or left one time. In so doing you will produce a wave pulse.
1) Sketch the resulting behavior of the slinky paying attention to how the pulse moves along the slinky.
2) Is there a net motion of the slinky?
The first type of pulse you launched was called a transverse pulse.
3) Explain the relationship between the direction the wave traveled and the direction of the disturbance in a transverse wave.
Sharply push the slinky inwards one time.
4) Sketch the behavior of the slinky paying attention to how the pulse moves along the slinky.
5) Is there a net motion of the slinky?
The second type of pulse you launched is called a longitudinal pulse.
6) Explain the relationship between the direction the wave traveled and the direction of the disturbance in a longitudinal wave.
7) If there is no net motion of the slinky, what does move when a wave travels along a slinky? Explain.
The slinky is called the medium through which the wave moves, and what moves through the medium is called a disturbance.
Place a light object like an empty soda can next to one end of the slinky. Create a transverse wave pulse by sharply shaking the slinky one time to the side opposite the light object.
8) Were you able to move the light object? (If not, position the object closer to the slinky and try again.)
9) If the light object was initially at rest and then began moving, it gained kinetic energy. Where did this energy come from? Does a wave carry energy?
With this series of observations, you have seen the basic behavior of all waves. Since there is no net motion of the slinky, we refer to the slinky as having been disturbed from its rest, or equilibrium position.
10) Complete the following: A wave is an ______which moves through a substance and which can transport ______.
Now, shake the slinky sideways continuously back and forth.
11) Sketch how the slinky appears.
When you make a continuous wave like you just did, it is called a wave train or else a continuous wave.
12) Was the wave train you created transverse or longitudinal?
13) Describe how you can move the slinky so that you produce a longitudinal wave train.
14) Carry out the procedure you described in 13) and sketch your results below.
15) Sketch a transverse continuous wave in the space below.
16) Sketch a longitudinal continuous wave in the space below.
Part 2: Speed of Waves
In part 3 of this activity, we will explore the dependence of the speed of a mechanical wave on a slinky on the tension in the slinky and the linear mass density of the slinky. We will make use of traveling waves like those we made in part 2. Traveling waves travel down the length of the slinky. In part 5 of this activity we will investigate another type of wave called a standing wave.
First determine the mass of the slinky.
1) m = ______kg
Now stretch the slinky on the floor a distance of 2 m for the shorter slinkies or 4 m for the longer ones. Have a person holding the slinky tightly at either end.
2) Record the length of the slinky: L = ______m
3) What is the mass per length (or the linear mass density) of the slinky?
Launch a single transverse pulse of the slinky and record the round trip time of the pulse. To obtain better data, repeat the measurement 6 times and find the average of your round trip times.
4) Record the average round trip time
5) Determine the speed of the wave on the slinky using = ______
6) Why is there a factor of two in the previous formula?
With the slinky stretched in the same way over the same distance, support one end of the slinky with the spring scale.
7) Record the tension in the slinky. Remember, the tension is a force, so use the correct scale on the spring scale.
The theoretical prediction for the speed of the wave on the slinky is given by
8) Calculate the theoretical prediction for the speed of the wave on the slinky
9) How do your values compare?
Part 3: Reflection and Interference of Waves
Hold the slinky at both ends. Launch a single transverse pulse and carefully observe how it appears after it is reflected. You might put a reference object near the end where the slinky reflects to help you make your observation.
1) Sketch a diagram showing how the wave pulse looked before and after the reflection.
Now hold on one end of the slinky with a ring stand so that the slinky is free to slide horizontally on the ring stand. Launch a single transverse pulse and carefully observe how it appears after it is reflected. This can be difficult to see so you may need to repeat several times until you are sure about what you are seeing. Also it helps to have a reference object near the end where the slinky reflects.
2) Sketch a diagram showing how the wave pulse looked before and after the reflection.
3) Compare how the reflected pulse compared to the incoming pulse for question 1) and 2).
There are two distinct ways that a wave can reflect at a boundary. One way is that the reflected wave is on the same side as the incoming wave. In this case, the reflected wave is in phase with the incident wave or we say that there is a phase difference of 0 between the two waves.
4) Did this occur for question 1) or 2)?
The second way is that the reflected wave is on the opposite side as the incoming wave. In this case, the reflected wave is 180 out of phase with the incident wave.
5) Did this occur for question 1) or 2)?
In question 1) we held the position of the slinky fixed. This is sometimes referred to as a fixed boundary condition.
6) Describe the phase of the reflected wave compared to the incident wave at a fixed boundary condition.
In question 2) we allowed the end of the slinky at the reflected end to move freely. This is sometimes referred to as a free boundary condition.
7) Describe the phase of the reflected wave compared to the incident wave at a free boundary condition.
Launch single transverse pulses simultaneously and on the same side from each end of the slinky. Observe what happens to the pulses when they meet in the middle. You might put a reference object near the middle where the two pulse meet to help you make your observation.
1) Sketch a diagram showing what happens to the pulses when they meet in the middle.
2) Do the pulses stop when they meet or do they continue moving?
The adding together of the two pulses in the middle is an example of what is called interference. When waves overlap, they simply add together. If the waves reinforce each other as in this case, we call the interference constructive.
3) Were the two pulses in phase or 180 out of phase?
4) Complete the following. Constructive interference occurs when the waves are ______phase.
Launch single transverse pulses simultaneously and on opposite sides from each end of the slinky. Observe what happens to the pulses when they meet in the middle. This can be difficult to see so you may need to repeat several times. You might put a reference object near the middle where the two pulse meet to help you make your observation.
5) Sketch a diagram showing what happens to the pulses when they meet in the middle.
6) Do the pulses stop when they meet or do they continue moving?
If the waves cancel each other as in this case, we call the interference destructive.
7) Were the two pulses in phase or 180 out of phase?
8) Complete the following. Destructive interference occurs when the waves are ______phase.
Part 4: Standing Waves
In this portion of the lab, we will produce standing waves on the slinky. We will determine the wavelength of the standing waves and the frequency and construct a graph to examine any relationship between the frequency of the standing waves and the wavelength. A standing wave is a wave that oscillates in time only but does not propagate like a traveling wave does. The standing wave oscillates back and forth between two extremes called the envelope of the standing wave. Figure 1 shows some envelopes of standing wave patterns with the wavelength of the standing wave related to the length. Figure 1 also depicts the nodes, the points that don't move, for each standing wave. We will use the number of nodes below to help us determine the wavelength of the standing waves that we had generated.
Figure 1 The first two envelopes (boundaries) between which standing wave patterns oscillate
Again stretch the slinky to a length of 2 m for short slinkies and 4 m for long ones. Hold one end of the slinky fixed and shake the slinky until the first pattern shown in figure 1 appears. Note this will only happen at a specific frequency.
1) Determine the frequency at which the slinky is being shaken. Accomplish this by timing 10 complete oscillations. The frequency will be given by f = 10/t
f = 10/t =
We can determine the wavelength from the geometry of the standing wave pattern. Notice that half of a wavelength fits in the distance L. Mathematically we can write this as /2 = L.
2) What is the wavelength for this standing wave?
Record your result in the table given below.
Repeat this measurement two more times, each time varying the wavelength and consequently the frequency of the waves. It is easier to determine the number of nodes than it is to directly determine the wavelength. The wavelength can be determined from the number of nodes as shown in figure 1.
TrialTime for 10 oscillations (t)Frequency (f=10/t)Nodes (n) Wavelength ()
3) Did the wavelength of the waves increase or decrease as you found standing wave patterns at higher frequencies?