A steel wire with mass 24.4 g and length 1.36 m is strung on a bass so that the

Question

A steel wire with mass 24.4 g and length 1.36 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

A) linear density= .0244/1.36= .0179
B) fundamental frequency=v/2L
so, 41.2 = v/2.2 => v = 90.64
C)f=(1/2L)[(F/)] so 41.2 = (1/2.2)[(F/.0179)]
=> v = 147.06 N
D)v=f => = v/f = 147.06 / 41.2 = 3.57 m.
E) = 343/41.2 = 8.33 m.

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