A steel wire with mass 27.3 g and length 1.56 m is strung on a bass so that the

Question

A steel wire with mass 27.3 g and length 1.56 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, 45.06 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

m = 27.3 g l = 1.56 m a.) u = m/l = 27.3 x 10^-3 / 1.56 = 1.75 x 10^-2 kg/m b.) f = 45.06 Hz => t = 1/f = 0.02193 sec, Therefore, V = d / t = 1.10 / 0.02193 = 50.16 m/s c.) V = sqrt (T/u) => T = V^2 x u = 50.16^2 x 1.75 x 10^-2 = 44.029 N d.) (Lamda)/2 = 1.10 m => Lamda = 2.20 m e.) For air, f = 45.06 Hz , V = 343 m/s , Thus, wavelength = V/f = 343/45.06 = 7.612 m

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