A guitar string with a mass of 12 g is 80 cm long and attached to a guitar at two points separated by 71 cm.What tension must the guitar string have so that its fundamental note is 256 Hz?
A)500 N
B)550 N
C)1100 N
D)2000 N
E)2200 N

Question

Quizplus · Accepted Answer

The formula for the frequency (f) of a string fixed at both ends is:

f = (1/2L) √(T/μ)

where L is the length of the string, T is the tension in the string, and μ is the linear mass density of the string (mass per unit length). We can solve this equation for the tension T:

T = (4Lf^2μ)

Given that the mass of the string (m) is 12 g and the length (L) is 80 cm, we can find μ:

μ = m/L = (12 g)/(80 cm) = 0.15 g/cm = 1.5 kg/m

Substituting this value for μ and the given frequency of 256 Hz into the equation for T, we get:

T = (4Lf^2μ) = (4 x 0.8 m x (256 Hz)^2 x 1.5 kg/m) ≈ 2000 N

So, the correct answer is D) 2000 N.

A Guitar String with a Mass of 12 G Is