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Q. 18

Expert-verified
Found in: Page 483

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

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

# The lowest note on a grand piano has a frequency of 27.5 Hz. The entire string is 2.00 m long and has a mass of 400 g. The vibrating section of the string is 1.90 m long. What tension is needed to tune this string properly?

The tension needed to tune the given string is .

See the step by step solution

## Given information

The frequency of the lowest note on a piano is .

The mass of the string is .

## Wavelength and wave speed

As the vibrating section of the string is long, the two ends of this vibrating wire are fixed, and the string is vibrating in the fundamental harmonic with wavelength

The wave speed along the string is

## Tension in the string

The linear density is given by

The wave speed is also given by .

Substitute the given values

Therefore, the tension in the string is .