   Chapter 14, Problem 47P

Chapter
Section
Textbook Problem

A steel wire with mass 25.0 g and length 1.35 m is strung on a bass so that the distance from the nut to the bridge is 1.10 m. (a) Compute the linear density of the string. (b) What velocity wave on the string will produce the desired fundamental frequency of the E1 string, 41.2 Hz? (c) Calculate the tension required to obtain the proper frequency. (d) Calculate the wavelength of the string’s vibration. (e) What is the wave-length of the sound produced in air? (Assume the speed of sound in air is 343 m/s.)

(a)

To determine
The linear density of the string.

Explanation

Given Info: The mass of the steel wire is 25.0g and length of the steel wire is 1.35m

Formula to calculate the linear density is,

μ=mL

• μ is the linear density of the string,
• m is the mass of the wire,
• L is the length of the wire,

Substitute 25.0g for m and 1.35m for L .

μ=(25

(b)

To determine
The velocity of the wave on the string.

(c)

To determine
The tension required to obtain the proper frequency in the string.

(d)

To determine
The wavelength of the string’s vibration.

(e)

To determine
The wavelength of the sound waves produced in air.

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