A steel wire with mass 21.1 g and length 1.22 m is strung on a bass so that the

Question

A steel wire with mass 21.1 g and length 1.22 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.
kg/m

(b) What velocity wave on the string will produce the desired fundamental frequency of the E1 string, 41.2 Hz?
m/s

(c) Calculate the tension required to obtain the proper frequency.
N

(d) Calculate the wavelength of the string's vibration.
m

(e) What is the wavelength of the sound produced in air? (Assume the speed of sound in air is 343 m/s.)
m

Explanation / Answer

part a )

linear density = mass / lenght

mass = 21.1 g = 0.0211 kg

length = 1.22 m

linear density = 0.0211 / 1.22 = 0.0173 kg / m

part b )

fundamental frequency = v/2L

v = f*2L

v = 41.2 * 2*1.1 = 90.64 m/s

part c ) v = sqrt (tension / linear density )

tension = v^2* linear density

tension = 142.13 N

d ) v = f*lambda

lambda = v/f

lambda = 90.64 / 41.2

lambda = 2.2 m

e ) c = flambda

lambda = c/f

c = velocity of sound in air

lambda = 343/41.2 = 8.325 m

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