Please include formulas for other applications, thanks. A steel wire with mass 2

Question

Please include formulas for other applications, thanks.

A steel wire with mass 25.5 g and length 1.16 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, 42.78 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

Part A)

Linear density, , is mass over length

.0255 kg/1.16 k = .022 kg/m   or 2.20 X 10-2 kg/m

Part B)

Using v = f

The wavelength for the fundamental frequency is twice the string lenght

v = (42.78)(2)(1.10)

v = 94.12 m/s

Part C)

v = (F/)

F = v2

F = (94.12)2(2.20 X 10-2)

F = 195 N

Part D)

= 2L

= (2)(1.1) = 2.2 m

Part E)

v = f

343 = 42.78

= 8.02 m

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