Answer: Music. You are designing a two-string instrument

QUESTION:

Music. You are designing a two-string instrument with metal strings \(35.0 \mathrm{~cm}\) long, as shown in Fig. P15.58. Both strings are under the . String \(S_{1}\) has a mass of \(8.00 \mathrm{~g}\) 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 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 this fret so that when you press \(S_{1}\) tightly against it, this string will produce C-sharp (frequency 277 Hz) in its fundamental? That is, what is in the figure?

(d) If you press \(S_{2}\)  against the fret, what frequency of sound will it produce in its fundamental?

Equation Transcription:

Text Transcription:

35.0 cm  

S_1  

8.00 g

S_2

S_1  

S_2