University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 15 - Mechanical Waves - Problems - Discussion Questions - Page 497: Q15.17

Answer

See explanation.

Work Step by Step

The fundamental frequency is given by equation 15.35. $$f_1=\frac{1}{2L}\sqrt{\frac{F}{\mu}}$$ In order to raise the pitch one octave, the fundamental frequency is multiplied by 2, so the tension F must be quadrupled, i.e., multiplied by 4. In order to raise the pitch two octaves, the fundamental frequency is multiplied by 4, so the tension F must be multiplied by 16. The danger in doing this is that the string/wire may snap under such a high tension.
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