Q7.

Expert-verified
Found in: Page 482

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# In music, two notes are said to be an octave apart when one note is exactly twice the frequency of the other. Suppose you have a guitar string playing frequency f0. To increase the frequency by an octave, to 2f0, by what factor would you have to (a) increase the tension or (b) decrease the length?

a) 4 times

b) 2 times

See the step by step solution

## Given information

Frequency of guitar string is being doubled by keeping everything constant except for a) Tension, b) length.

## Part a): Dependency on Tension

We can see frequency is directly proportional to square root of tension. So in order to increase frequency by 2 times we have to increase the tension in the string by 4 times.

## Part b): Dependency on Length

We can see frequency is inversely proportional to the length of string, so to increase the frequency by 2 times, length has to be decrease by 2 times (or halved).