Chapter 12, Problem 13ICA

The vibrating frequency of a guitar string depends on tension, length, and mass per unit length of the string. The equation for the fundamental frequency of a vibrating string is given by

$\text{f=}\frac{\sqrt{T/\mu }}{2L}$

Where

f = frequency [Hz]

T = string tension [N]

µ =- mass per unit length [kg/ m]

L = string length [    m]

Many electric guitars have a device often called a "whammy" bar or a "tremolo" bar that allows the guitarist to change the tension on the strings quickly and easily, thus changing the frequency of the strings. (Think of Jimi Hendrix simulating "the rockets red glare, the bombs bursting in air" in his rendition of The Star Spangled Banner-a true tour de force.) In designing a new whammy bar, we test our design by collecting data using a single string on the guitar and creating a graph of the observed frequency at different string lengths as shown.

1. a. Is the relationship between frequency and length linear, power, or exponential?
2. b. What are the units of the coefficient (108)?
3. c. If the tension on the string is 135 newtons, what is the mass per unit length in grams per meter?
4. d. If the mass per length of the string is 3.5 grams per meter, what is the tension in newtons?