PhysicsLAB: Speed of a Wave Along a Spring

Equipment

In this lab you will need several stop watches, one long spring, one 20-N spring scale, meter sticks for measuring as well as 2-loop makers, 3-loop markers, 4-loop markers.

Attach one end of your long spring to a table by slipping it over the pole of a well-secured ring stand.

Part I - 20 foot separation

Stretch the spring approximately 20 feet, which equals 6.1 meters. Remember that each floor tile is 1 ft². Use a 20-N spring scale to measure the tension in the spring. Do NOT move from this position until Part I of the experiment is finished.

What was the tension on your spring scale?

Send a LARGE amplitude horizontal pulse down the spring. Record the time for it to make three complete vibrations or trips. Time a total of three pulses. Record your values in the table below.

pulse trial

time (sec)

What was the average time for the pulse to make three complete vibrations?

Calculate the speed of the pulse along the spring using the equation d = rt where d = 6(6.1) meters and t is your average time for three complete trips recorded above.

When a periodic wave is sent down a spring, special frequencies produce loops, or regions of constructive and destructive interference. A loop equals one-half of a wavelength, ½l.

We are now going to vibrate the spring at three different frequencies: the first one will produce two loops, the second one will produce three loops, and the fourth one will produce 4 loops.

Each time the desired pattern is produced, we will place meter sticks on the floor under two adjacent nodes. Nodes are easily identified as locations where there is NO amplitude - where the wave form seems to stay squeezed together.

Next we will time 5 complete vibrations of the spring while maintaining two loops. Record your times in the table below.

2-loop trial

time (sec)

What was the length of a single loop when there are two loops along the spring?

What was the average time for your spring to make 5 complete vibrations when two loops were on the spring?

Next we will time 5 complete vibrations of the spring while maintaining three loops. Record your times in the table below.

3-loop trial

time (sec)

What was the length of a single loop when there are three loops along the spring?

What was the average time for your spring to make 5 complete vibrations when three loops were on the spring?

Next we will time 5 complete vibrations of the spring while maintaining four loops. Record your times in the table below.

4-loop trial

time (sec)

What was the length of a single loop when there are four loops along the spring?

What was the average time for your spring to make 5 complete vibrations when four loops were on the spring?

Part II - Doubling the Tension

Stretch the spring approximately 31.5 feet, which equals 9.6 meters. Remember that each floor tile is 1 ft². Use a 20-N spring scale to measure the tension in the spring. Do NOT move from this position until Part II of the experiment is finished.

What was the tension on your spring scale?

Send a LARGE amplitude horizontal pulse down the spring. Record the time for it to make three complete vibrations or trips. Time a total of three pulses. Record your values in the table below.

pulse trial

time (sec)

What was the average time for the pulse to make three complete vibrations?

Calculate the wave speed in the spring using the equation d = rt where d = 6(9.6) meters and t is your average time for three complete trips recorded above.

Next we will time 5 complete vibrations of the spring while maintaining two loops. Record your times in the table below.

2-loop trial

time (sec)

What was the length of a single loop when there are two loops along the spring?

What was the average time for your spring to make 5 complete vibrations when two loops were on the spring?

Next we will time 5 complete vibrations of the spring while maintaining three loops. Record your times in the table below.

3-loop trial

time (sec)

What was the length of a single loop when there are three loops along the spring?

What was the average time for your spring to make 5 complete vibrations when three loops were on the spring?

Next we will time 5 complete vibrations of the spring while maintaining four loops. Record your times in the table below.

4-loop trial

time (sec)

What was the length of a single loop when there are four loops along the spring?

What was the average time for your spring to make 5 complete vibrations when four loops were on the spring?

Calculations

Part I:
loops

frequency
(hz)

loop length
(m)

wavelength
(m)

wave speed
(m/sec)

Part II:
loops

frequency
(hz)

loop length
(m)

wavelength
(m)

wave speed
(m/sec)

Conclusions

1. What was the average wave speed in Part I when 2, 3, and 4 loops were maintained on the spring? (Chart I)

2. Calculate the percent difference between the speed of the pulse in Part I (20 foot separation) and the average wave speed from Chart I.

3. What was the average wave speed in Part II when 2, 3, and 4 loops were maintained on the spring? (Chart II)

4. Calculate the percent difference between the speed of the pulse in Part II (doubling the tension) and the average wave speed from Chart II.

5. Calculate the ratio of the average wave speed in Part I (question #1) and in Part II (question #2).

Fill in the blanks in the last three questions with one of the following terms: decreases, remains the same, increases, smaller, larger

6. In the same medium (20-foot separation or doubling the tension) the wave speed ______

8. As the tension in a spring increases, the wave speed _______.

7. In a given medium (either a 20-foot separation or doubling the tension), as the frequency increases, the wavelength ______ as shown by a _______ loop length.