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A vibration is a wiggle in time; a wave is a wiggle in space and time. In this exercise, you will explore that connection by transferring the motion of the second hand of a clock (a vibration, even if a slow one), to a wave.

Print out the image of a clock and open the spreadsheet called Grapher. You will find both of them in the same item where you found these instructions.

Use a metric ruler to measure the displacement of the tip of the second hand every five seconds. That’s the distance above or below the center line that connects the 3 and the 9. Count the number as positive if the tip is above the line (towards the 12) and negative if below (towards the six). Enter each value in the tinted boxes in the Grapher tool and it will immediately plot them for you.

Then answer the questions based on your graph.

1) What is the period of this wave, that is, the time for one complete cycle, in seconds? The period of the wave is .02 seconds

2) What is the amplitude of the wave?

The amplitude is .01

3) If we had started from some other initial position – say, when the second hand was on the 3 – would the period still be the same?

no

yes X

4) Again, if we had started when the second hand was on the 3, would the amplitude still be the same?

no

yes X

5) So – again, if we had started when the second hand was on the 3, what would be different? Though we are starting from a later point, the period would still be the same distance, and amplitude is reliant on the period so if the period is the same then so is the amplitude. Simply the seconds from which we start measuring would be one notch behind, so the arch of each wave would be 5 seconds earlier.

6) Using the period from question 1, find the frequency of the wave. That frequency is of course way too low for us to hear. Please round you answer to three digits, not counting the starting zero; that is, round it to four decimal places total.

The frequency is .0125 Hz

7) If you had used the same picture of the same clock but had graphed the minute hand instead, what would change about the graph?

Nothing would change at all.

The frequency would change.

The amplitude would change. X

8) If you had plotted the motion of the second hand on your watch instead of the clock that you printed out, what would change about the graph?

Nothing would change at all.

The frequency would change. X

The amplitude would change.

9) Since you are plotting displacement on the y-axis and time on the x-axis, this is an example of a _____ graph.

Snapshot X

frog-on-a-post

10) Are you old enough to remember the 90’s television series Home Improvement, starring Tim Allen? He was always saying “more power” and blowing up one electric tool or appliance after another by trying to make it work faster.

Suppose that he was able to make a clock run so fast that the second hand made one full lap in only one-tenth of a second (0.10 s), and suppose that it tapped a water surface each time it reached the bottom of its motion. If the waves it produced were 4.0 cm apart, at what speed (in cm/s) would they travel?

The Waves would travel 40cm/s