You are designing a two-string instrument with metal strings 35.0 cm long as sho

Question

You are designing a two-string instrument with metal strings 35.0 cm long as shown in the figure. Both strings are under the same tension. String S_1 has a mass of 8.00 g and produces the note middle C (frequency 262 Hz) in its fundamental mode

a)What should be the Tension in the string?

b) What should be the mass of the string S_2 so that it will produce A-Sharp (frequency 466 Hz) as its fundamental?

c)To extend the range of your instrument, you include a fret located just under the strings but not normally touching them. How far from the upper end should you put the fret so that when you press S_1 tightly against it, this string will produce a C-Sharp (frequency 277 Hz) in its fundamental? That is, What is x in the figure?

d) If you press S_2 against the fret, what frequency of sound will it produce in its fundamental?

Explanation / Answer

f = 1/2L(sq rt F/mu) 262 hz = 1/2(0.35 m) (sqrt F/0.0083 kg) F = 279 N 466 hz = 1/2(0.35 m)(sqrt 279/mu) mu = 2.6 g/m 277 = 1/2(L) (sqrt 279/0.0083 kg) L = 33.1 cm (35 - 33.1 = 1.9 cm from the end) f = 1/2(0.331)(sqrt 279/0.0026) f = 495 hz

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