A steel wire with mass 24.9 g and length1.61 m is strung on a bass so that thedi

Question

A steel wire with mass 24.9 g and length1.61 m is strung on a bass so that thedistance from the nut to the bridge is 1.10 m. (a) Compute the linear density of thestring.
kg/m

(b) What velocity wave on the string will produce the desiredfundamental frequency of the E1 string, 33.33 Hz?
m/s

(c) Calculate the tension required to obtain the properfrequency.
N

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

(e) What is the wavelength of the sound produced in air? (Assumethe speed of sound in air is 343 m/s.)
m (a) Compute the linear density of thestring.
kg/m

(b) What velocity wave on the string will produce the desiredfundamental frequency of the E1 string, 33.33 Hz?
m/s

(c) Calculate the tension required to obtain the properfrequency.
N

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

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

Explanation / Answer

(a) Compute the linear density of thestring.
kg/m
linear density24.9*10-3/1.61=15.46*10-3kg/m

(b) What velocity wave on the string will produce the desiredfundamental frequency of the E1 string, 33.33 Hz?
m/s
fundamentalfrequency=33.33=v/2l=v/2*1.1=>v=2*1.1*33.33=73.326m/sec

(c) Calculate the tension required to obtain the properfrequency.
1/2.2*T/15.46*10-3=33.33
calculating T=83.12N
N

(d) Calculate the wavelength of the string's vibration.
m
wavelength=2*l=2.2m

(e) What is the wavelength of the sound produced in air? (Assumethe speed of sound in air is 343 m/s.)
m
wavelength=velocity/frequency=343/33=10.39m

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