Question

The 6 strings on a guitar all have about the same length and are stretched with about the same tension.The highest string vibrates with a frequency that is 4 times that of the lowest string.

If the strings are made of the same material, how would you expect the diameters of the lowest and highest strings to compare?

A. d(low)=2d(high)

B. d(low)=4d(high)

C. d(low)=16d(high)

Answer 1

f is propotional to v/l

since l is same f is propotional to v

v = sqrt(T/u)   u=mass / length

T is same

v is prop to 1/sqrt(u)

u= m/l

l is same

m is propotional to Volume which is propotional to r²*l

f is prop to 1/sqrt(m) = 1/sqrt(r²)

u is prop to r²

f is hence prop to 1/r

hence d(low) = 4*d(high)