After you retire, you decide to become a guitar tuner. But, to tune a guitar wel
ID: 1313132 • Letter: A
Question
After you retire, you decide to become a guitar tuner. But, to tune a guitar well, you need to understand the physics of guitar tuning. You begin by tightening the guitar strings that are made of steel (Young's modulus = 2.0 x 10^11 N/m^2). One end of the steel string is wrapped around a tuning peg that is a cylinder of radius 4.0 mm. When you turn the peg using a knob on the side of the guitar, you are applying a force on the string because of which the length of the string increases. Before you turn the knob, the guitar string has an original length of 0.70 m and a radius of 0.2mm. Find the tension force acting on the guitar string when you turn the tuning peg through two revolutions. Consider the radius of the wire to be very small compared to the radius of the tuning peg. Hint: calculate the circumference of the tuning peg.
Explanation / Answer
Area of cross section of wire, A = pi * r^2 = 3.14 * (0.2*10^-3)^2 = 0.0000001256 m^2
Initial length of wire = L0 = 0.7m
Circumference of tuning peg = 2* pi * R = 2* 3.14 * 4 *10^-3 = 0.02512 m
Increase in length of wire, dL = 2* Circumference of tuning peg = 2* 0.02512 = 0.05024 m
According to Hooke's law,
Tension = Young's modulus * A * dL / L0 = 2 * (10^11) * 0.0000001256 * 0.05024 / 0.7 = 1802.898 N
tension force acting on the guitar string = 1802.898 N is the answer.