You are designing a two-string instrument with metal strings 35.0 cm long, as shown in Fig. P15.58. Both strings are under the same tension. String S₁has 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 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 against the fret, what frequency of sound will it produce in its fundamental?

Figure P15.58:

Transcribed Image Text:

Fret 35.0 cm S2 S1 (C) (A*)