Scale length is the length of the part of a guitar string that is free to vibrate. A standard value of scale length for an acoustic guitar is 25.5 in. The frequency of the fundamental standing wave on a string is determined by the string€™s scale length, tension, and linear mass density. The standard frequencies f to which the strings of a six-string guitar are tuned are given in the table:

Assume that a typical value of the tension of a guitar string is 78.0 N (although tension varies somewhat for different strings).

(a) Calculate the linear mass density µ (in g/cm) for the E2, G3, and E4 strings.

(b) Just before your band is going to perform, your G3 string breaks. The only replacement string you have is an E2. If your strings have the linear mass densities calculated in part (a), what must be the tension in the replacement string to bring its fundamental frequency to the G3 value of 196.0 Hz?

Transcribed Image Text:

String E2 A2 G3 ВЗ E4 D3 f (Hz) | 82.4 110.0 146.8 196.0 246.9 329.6