Chapter 12, Problem 17P

A physics student suspends a 1 kg mass from a pulley using a wire as shown in Figure 12.39. The pulley allows her to easily change the length of the wire. In order to determine the speed of a transverse wave on the wire, she measures the frequency of the fundamental mode as a function of the length of the wire L. The table shows her results:

Figure 12.39 Problem 17.

Make two plots of these data. First plot the frequency as a function of L, and then plot it as a function of 1/L. Which graph shows a linear relationship? Draw a best-fit line through the linear graph’s data, and use the slope of this line to determine the wave speed.

12.17. Set Up: The fundamental frequency satisfies $f_1=\frac{v}{2L}$. A plot of frequency versus length with therefore have a slop $s=\frac{v}{2}$.

Solve: (a) The frequency as a function of string length is plotted below.

The frequency as a function of the inverse of the string length is plotted below.

The frequency in linear when plotted as a function of inverse length. The slope of the best-fit line is s = 49.2 m/s. The wave speed is thus v = 2s =2(49.2 m/s) = 98 m/s.