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Chapter 16: Q. 62 (page 453)

The G string on a guitar is a 0.46-mm-diameter steel string

with a linear density of 1.3 g/m. When the string is properly

tuned to 196 Hz, the wave speed on the string is 250 m/s. Tuning

is done by turning the tuning screw, which slowly tightens鈥攁nd

stretches鈥攖he string. By how many mm does a 75-cm-long G

string stretch when it鈥檚 first tuned?

Short Answer

Expert verified

The G-string stretch by a length of 1.8mmwhen it鈥檚 first tuned.

Step by step solution

01

given data

Length of the string, L=75cm=0.75m.

Wave speed on the string, v=250m/s

Diameter of the steel string, d=0.46mm=4.6脳10-4m

The linear density of the string is,渭=1.3g/m=0.0013kg/m.

02

Determination of tension force

The tension force can be obtained by using the equation,

v=T渭

Therefore, the tension force is,

T=v2渭鈬�T=250m2脳0.0013kg/m鈬�T=81.25N

The Young modulus of steel string can be considered as,

Y=2脳1011N/m2

Thus, the G-string will be stretched by an amount of 鈭�Lwhich can be obtained by,

鈭�L=LTY蟺r2鈬�鈭�L=0.75m脳81.25N2脳1011N/m2脳蟺d22鈬�鈭�L=0.75m脳81.25N2脳1011N/m2脳蟺4.6脳10-42m2鈬�鈭�L=0.0018m鈬�鈭�L=1.8mm

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