Answer to Question #184984 in Civil and Environmental Engineering for John Prats

Question

Two string A and B are given. The length if A is twice that of B. The total mass if A is one-third that of B. If the tension in wire A is one-half that of B and the fundamental frequency of A is 400 Hz, what is the fundamental frequency of string B?

Answer 1

Fundamental frequency of string is given by f1 = ½(F/LM)^1/2

Fundamental frequency is directly proportional to square root of Force or tension

And inversely proportional to square root of Mass and inversely proportional to square root of length.

Given that fundamental frequency of A is 400 Hz

Then due to effect of length,

Fundamental frequency of B is 400*1/√0.5=565.68 Hz

Due to mass

Fundamental frequency=565.68/√3=326.98

Due to tension

Fundamental frequency= 326.98√2=462.42 Hz

Thus fundamental frequency of B is 462.42Hz