The B-string of a guitar is made of steel (density 7800 kg/m3), is 63.5 cm long, and has diameter 0.406 mm. The fundamental frequency is f= 247.0 Hz.
(a) Find the string tension.
(b) If the tension F is changed by a small amount ΔF, the frequency f changes by a small amount ΔF Show that


(c) The string is tuned as in part (a) when its temperature is 18.5oC.Strenuous playing can make the temperature of the string rise, changing its vibration frequency. Find ΔF if the temperature of the string rises to 29.5oC. The steel string has a Young's modulus of 2.00 X 10" Pa and a coefficient of linear expansion of1.20 X 1011 (Co) 1. Assume that the temperature of the body of the guitar remains constant. Will the vibration frequency rise or fall?

Transcribed Image Text:

Af 1 Af S 2f