A guitar string is 92 cm long and has a mass of 3.4 g. The distance from the bridge to the support post is l = 62 cm, and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?
In order to watch this solution you need to have a subscription.
This is Giancoli Answers with Mr. Dychko. The resonant frequencies are n times the wave speed in the string divided by 2 times the length of string that's resonating. And the wave speed is gonna be the tension force divided by the mass per unit length, all square rooted. And mass per unit length is the mass of the string divided by its total length. And I put the subscript T for total to distinguish it from this length here which is the vibrating length so, when we have, when we substitute this μ in place and write in l or lT over lm, this l here is, lT is 92 centimeters. Whereas the l on the bottom is the resonating length which is 62 centimeters. I'm going to write this division by μ as multiplying by its reciprocal. So, we multiply by total length over m. And so finding the fundamental means we put in 1 for n and times by square root of 520 newtons times 92 times 10 to the minus 2 meters divided by 3.4 times 10 to the minus 3 kilograms converting all these units into meters and kilograms divided by 62 times 10 to minus 2 meters times 2. And that gives about 300 hertz. And the second resonant frequency or the first overtone is 2 times the fundamental, 2 times 302.51 which rounds to 610 hertz. And then the third resonant frequency is 910 hertz.
Find us on:
