Question

segments over the length L of the string, where the length of each vibrating segment equals one-half wavelength. Use this fact to show that the fr of the allowed standing waves on this string are given by fn-nfi, where n 1,2,3, 4,5,... and fi is the fundamental frequency. In other words, derive an expression relating the nth harmonic to the fundamental frequency. Yo may use the fact that the wave velocity is the same for all modes. 1. For a string with both ends fixed, the nth allowed standing wave has n vibrat 2. Assume that the general mathematical relation between two quantities y and is given by a power law. That is, where A is a constant and N is the power. Show that log(v)- N log(x) + log(A) where log is the base-10 logarithm. Explain why a straight line will result if you plot log() [y-axis] vs. log(x) [r-axis]. How can you determine A and N from this straight line? As a particular example of this technique, consider a stretchable string, which has a constant mass m, but a variable length D that depends on the tension T in the string. Then, remembering that the strings nnass per length μ m/D. the velocity v of waves on this string is given by TD Show that if log(v) is plotted vs. log(TD), then the resulting straight line wil give slope 1/2 and m 10-2b where b is the y-intercept.

Answer 1