# Chapter 21 - Superposition - Exercises and Problems: 10

(a) $f_1 = 12~Hz$ $v = 24~m/s$ (b) The image shows the standing wave pattern for the fourth harmonic, which is 48 Hz.

#### Work Step by Step

(a) Let $f_{n+1} = 48~Hz$ and let $f_n = 36~Hz$. We can find the fundamental frequency: $f_{n+1} = (n+1)~f_1$ and $f_n = n~f_1$ $f_{n+1}- f_n = (n+1)~f_1 - n~f_1 = f_1$ Therefore, $f_1 = f_{n+1}-f_n$ $f_1 = 48~Hz-36~Hz = 12~Hz$ We can find the wave speed. $v = f_1~\lambda_1$ $v = (f_1)(2L)$ $v = (12~Hz)(2)(1.0~m)$ $v = 24~m/s$ (b) The image shows the standing wave pattern for the fourth harmonic, which is 48 Hz.

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