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A string is vibrating back and forth as in Figure 17. l 8a. The tension in the string is decreased by a factor of four, with the frequency and the length of the string remaining the same. Draw the new standing wave pattern that develops on the string. Give your reasoning.

A string is vibrating back and forth as in Figure 17. l 8a. The tension in the string is decreased by a factor of four, with the frequency and the length of the string remaining the same. Draw the new standing wave pattern that develops on the string. Give your reasoning.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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A string is vibrating back and forth as in Figure 17. l 8a. The
tension in the string is decreased by a factor of four, with the frequency and the length of the string remaining the same. Draw the
new standing wave pattern that develops on the string. Give your
reasoning. 

Frequency - 1st harmonic (fundamental) (a) -Antinodes- Frequency = 2j 2nd harmonic (1st overtone) (b) 3rd harmonic (2nd overtone) Frequency = 3ji (c) Figure 17.18 Vibrating a string at certain unique frequencies sets up transverse standing wave patterns, such as the three shown in the photographs on the left. Each drawing on the right shows the various shapes that the string assumes at various times as it vibrates. role that this simple but powerful principle has played in this chapter. It is an expansion of the charts in Figures 17.9 and 17.14. 4 Figure 17.18 shows some of the essential features of transverse standing waves. In this figure the left end of each string is vibrated back and forth, while the right end is at- tached to a wall. Regions of the string move so fast that they appear only as a blur in the photographs. Each of the patterns shown is called a transverse standing wave pattern. Notice that the patterns include special places called nodes and antinodes. The nodes are places that do not vibrate at all, and the antinodes are places where maximum vibration occurs. To the right of each photograph is a drawing that helps us to visualize the motion of the string as it vibrates in a standing wave pattern. These drawings freeze the shape of the string at various times and emphasize the maximum vibration that occurs at an antin- ode with the aid of a red dot attached to the string. The red dots attached to the strings focus attention on the maximum vibration that occurs at an antinode. In each of the drawings, one-half of a wave cycle is outlined in red. (Richard Megna/Fundamenta! Photographs)
Transcribed Image Text:Frequency - 1st harmonic (fundamental) (a) -Antinodes- Frequency = 2j 2nd harmonic (1st overtone) (b) 3rd harmonic (2nd overtone) Frequency = 3ji (c) Figure 17.18 Vibrating a string at certain unique frequencies sets up transverse standing wave patterns, such as the three shown in the photographs on the left. Each drawing on the right shows the various shapes that the string assumes at various times as it vibrates. role that this simple but powerful principle has played in this chapter. It is an expansion of the charts in Figures 17.9 and 17.14. 4 Figure 17.18 shows some of the essential features of transverse standing waves. In this figure the left end of each string is vibrated back and forth, while the right end is at- tached to a wall. Regions of the string move so fast that they appear only as a blur in the photographs. Each of the patterns shown is called a transverse standing wave pattern. Notice that the patterns include special places called nodes and antinodes. The nodes are places that do not vibrate at all, and the antinodes are places where maximum vibration occurs. To the right of each photograph is a drawing that helps us to visualize the motion of the string as it vibrates in a standing wave pattern. These drawings freeze the shape of the string at various times and emphasize the maximum vibration that occurs at an antin- ode with the aid of a red dot attached to the string. The red dots attached to the strings focus attention on the maximum vibration that occurs at an antinode. In each of the drawings, one-half of a wave cycle is outlined in red. (Richard Megna/Fundamenta! Photographs)
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