Two wires are stretched between two fixed supports and have the same length. On

Question

Two wires are stretched between two fixed supports and have the same length. On wire A there is a second-harmonic standing wave whose frequecy is 660 Hz. However, the same frequency of 660 Hz is the third harmonic on wire B. (a) Is the fundamental frequecy of wire A greater than, less than, or equal to the fundamental frequency of wire B? Explain. (b) How is the fundamental frequency related to the length L of the wire and the speed v at which individual waves travel back and forth on the wire? (c) Do the individual waves travel on wire A with a greater, smaller, or the same speed as on wire B? Give your reasoning.

Explanation / Answer

Consider two wires having the same length LA =LB = L The fundamental frequency of wire A is f1A = VA / 2LA The second harmonic frequency of wire A is f2A =2f1A = 660Hz ==> f1A = 330Hz The fundamental frequency of wire B is f1B = VB / 2LB The third harmonic frequency of wire B is f3B =3f1B = 660Hz ==> f1B = 220Hz (a) The fundamental frequency of wire A is greater than wireB. (b) f = V / 2L (c) VA = f1A * L = 330L and VB = f1B * L = 220L        so that waves in wire Atravels with greater speed.

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