Chapter 15, Problem 15.54P

Music. You are designing a two-string instrument with metal strings 35.0 cm long, as shown in Fig. P15.54. Both strings are under the same tension. String S₁ has a mass of 8.00 g and produces the note middle C (frequency 262 Hz) in its fundamental mode. 35.0 cm (a) What should be the tension in the string? (b) What should be the mass of string S₂ 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 S₁ tightly against it, this string will produce C-sharp (frequency 277 Hz) in its fundamental? That is, what is x in the figure? (d) If you press S₂ against the fret, what frequency of sound will it produce in its fundamental?

Figure P15.54