The fundamental frequency of a vibrating guitar string is modeled by the following equation: $$f = \frac { 1 } { 2 L } \sqrt { \frac { T } { \mu } }$$
where
$$\begin{array} { l }
f = \text { vibration frequency in hertz } \
L = \text { length of string in meters } \
T = \text { string tension in newtons } \
\mu = \text { string density }
\end{array}$$
What is the appropriate unit for $\mu$ if the preceding equation is to be homogeneous in units?

Question

The fundamental frequency of a vibrating guitar string is modeled by the following equation: $$f = \frac { 1 } { 2 L } \sqrt { \frac { T } { \mu } }$$
where
$$\begin{array} { l } 
f = \text { vibration frequency in hertz } \
L = \text { length of string in meters } \
T = \text { string tension in newtons } \
\mu = \text { string density }
\end{array}$$
What is the appropriate unit for $\mu$ if the preceding equation is to be homogeneous in units?

Quizplus · Accepted Answer

The Answer of The fundamental frequency of a vibrating guitar string is modeled by the following equation: $$f = \frac { 1 } { 2 L } \sqrt { \frac { T } { \mu } }$$
where
$$\begin{array} { l } 
f = \text { vibration frequency in hertz } \
L = \text { length of string in meters } \
T = \text { string tension in newtons } \
\mu = \text { string density }
\end{array}$$
What is the appropriate unit for $\mu$ if the preceding equation is to be homogeneous in units?

The Fundamental Frequency of a Vibrating Guitar String Is Modeled f=12LTμf = \frac { 1 } { 2 L } \sqrt { \frac { T } { \mu } }f=2L1​μT​​

The Fundamental Frequency of a Vibrating Guitar String Is Modeled $f = \frac { 1 } { 2 L } \sqrt { \frac { T } { \mu } }$