# Lenght and Frequency of a String

One type of steel has a density of 8000 kg/m^3 and a breaking stress of 7.1×108 N/m^2. A cylindrical guitar string is to be made out of a quantity of steel with a mass of 4.50 g.

a). What is the length of the longest and thinnest string that can be placed under a tension of 890 N without breaking?

b). What is the highest fundamental frequency that this string could have?

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#### Solution Preview

a) (4.50g)*(1kg/1000g)*(7.1x10^8 N/m^2)/(8000kg/m^3)*(890 N) = 0.449 m = 449 ...

#### Solution Summary

Lenght and frequency of a cylindrical guitar string is determined in the solution.

Harmonic frequency, tension force, length of string

SEE ATTACHMENT #1 for the general form of the equation of standing waves.

A standing wave is set up in a guitar string. Find the first harmonic frequency. Then for a new frequency find new string tension and length.

A guitar string is .64 m long and has a linear density of .0004 kg/m. The tension is set at 55 newtons.

PART a. Find the frequency of the first harmonic, the fundamental note emitted.

PART b. Find the tension force required for the string to emit a fundamental note, or first harmonic, of 350 cy/sec.

PART c. With tension at 55 nt, you press a fret to shorten the length for which the fundamental is 350 cy/sec. Find the new length.