Question

A steel wire with mass 23.6 g and length 1.19 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 E_1 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

Answer 1

Given that

mass m=0.0236 kg

length L=1.19 m

distance x=1.1 m

now we find the lineat density of the string

linear density $\mu$ =[0.0236/1.19]=0.0198 kg/m

now we find the velocity

frequency =V/2x

41.2=V/2*1.1

velocity v=90.64 m/s

now we find the tension required to obtain proper frequency

tension T=90.64^2*0.0198=162.7 N

now we find the wavelength of the string's vibration

wavelength =90.64/41.2=2.2 m

now we find the wavelength of the sound produced in air

the wavelength of the sound =343/41.2=8.33 m