FORMAL WRITEUP

PURPOSE: To determine the relationship between tension and pitch, and to investigate the physics behind the sound generated by stringed instruments, and in this case, an acoustic guitar.

OBJECTIVE: To develop an understanding of how pitch can relate to string length, string tension, and the gauge(thickness)of the string.

HYPOTHESIS: I predict that the string with the lowest tension will have the highest pitch. I also predict that the thickest string will produce the lowest pitch.

MATERIALS:

• 1 – rectangular sound box (I used an empty cigar box I picked up from a vendor).

• 4 – 4’ lengths of nylon fishing line that are 4 lb. strengths

• 4 – 4’ lengths of nylon fishing line – 1 each of 4, 10, 15, and 20 lb. strengths

• 4 – push pins

• 2 – triangular rulers such as an architect’s rule or a triangular length of wood longer than the box is wide (a pencil or similar sized object may work, but a triangular shape works best)

• 4 – 200-gram weights (lead fishing sinkers will work)

• 4 – increasingly heavier weights – 100-gram, 200-gram, 300-gram and 400-gram are ideal for this lab. Fishing sinkers make a good substitute for laboratory weights. (Note: 100 grams = approx. 3.5 oz.)

• 1 – guitar pick.

PROCEDURE:

1. Gather materials. Make special note of the difference in thickness of strings. Take the lengths of line and cut them into the appropriate lengths.

2. Take the sinkers and place them in bundles to create 100, 200, 300, and 400 gram weights.

3. Tie a knot in one end of each length of fishing test line.

4. Get the four 4-lb. test lines. To one of these lines, tie a 100-gram weight to the unknotted end. Repeat this procedure for the three other 4-lb. test lines with the 200-gram, 300-gram, and 400-gram weights.

5. Take the 4, 10, 15, and 20-lb. test lines and tie a 200-gram weight to the unknotted end of each of these lines.

6. Make four evenly spaced marks across the narrow end of the cigar box. This is where the end of your “guitar” strings will be attached.

7. Take the four, 4-lb. test lines with increasing weights. Insert a push pin through the knot at the end of each line and attach, in order of increasing weight, to the end of the cigar box.

8. Place the box near the edge of a table so the weights can hang freely. Support all four of the strings by placing the bridge material underneath the strings near each end of the box parallel to the end of the box.p>
9. Using the pick, gently strum each string individually between the bridges. (Note that all strings are of equal thickness but under different tensions.)

10. Remove the pins/tacks. Locate the set of lines with equal weights but different thickness. Attach these lines, in order of increasing thickness, to the end of the box using the push pins/tacks as done before in Step 6.

11. Place the box near the edge of the table so the weights can hang freely. Place the bridge material underneath the strings near each end of the box.

12. Gently strum each line individually with the pick beginning with the thickest string and ending with the thinnest. (Note that all strings are under the same tension.)
    OBSERVATIONS: In the first part of the experiment I noticed that the variable of tension was responsible for the change in pitch. It was found that the lowest tension produced the lowest pitch. In the second part of the experiment it was the thickness of the string (all strings under the same tension) that was responsible for the change in pitch. It was found that the thickest/heaviest string generates the lowest pitch. In music this is known as the gauge of the string. An interesting observation made during the experiment was that when the rulers were slid closer to each other, effectively decreasing the string length, the pitch increased. This was true to the opposite also. When the rulers were slid farther apart from each other, the pitch decreased, as the string length was lengthened.
    RESULTS:

    In the end, the experiment turned out the way I had predicted, therefore my hypothesis was correct. The string's tension affected the pitch, for when the tension was increased, the pitch increased proportionately. Out of all the strings with the same thickness, with differing tensions, the tension was directly proportional to the pitch. As far as the other half of the experiment, the tensions were the controlled variable, and the thicknesses of the strings were altered. It was found that the thicker the string was, the lower the pitch.

    

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