A steel wire with mass 20.7 g andlength 1.11 m is strung on a bass sothat the di

Question

A steel wire with mass 20.7 g andlength 1.11 m is strung on a bass sothat the distance from the nut to the bridge is 1.10 m. (a) Compute the linear density of thestring.
1 kg/m

(b) What velocity wave on the string will produce the desiredfundamental frequency of the E1 string, 44.54 Hz?
2 m/s

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

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

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

(b) What velocity wave on the string will produce the desiredfundamental frequency of the E1 string, 44.54 Hz?
2 m/s

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

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

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

Explanation / Answer

1) M / L = .0207 / 1.11 = .0186 kg / m 2) With a node at either end the wavelength isgiven by        L = N /2     an integral number of / 2     For N = 1 = 2.2 m v = f = 44.54 * 2.2 = 98 m / s 3) v = (F / (M / L)) F = v2 * (M / L) = 982 * .0186 =179 N 4) = v / f = 98 / 44.54 = 2.2m      which is the fundamental wavelengthas stated above 5) s = 343 / 44.54 = 7.7m      the wavelength of the sound waveproduced

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