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Q. 18

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 483

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Short Answer

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 .

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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 .

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