A length of piano wire is used to hang a mass from the ceiling.If the total mass of the string is 0.72 g and the mass hung from it is 1850 g,what is the length of the wire,assuming the fundamental frequency when plucked in these circumstances is 1280 Hz?
A) 2.48 cm
B) 6.15 cm
C) 3.08 cm
D) 1.54 cm

Question

Quizplus · Accepted Answer

We can use the formula:

f = (1/2L) * sqrt(Tension/linear density)

where:
f = fundamental frequency = 1280 Hz
L = length of the wire
Tension = weight of the mass = (1850 g) * (9.8 m/s^2) = 18130 N
linear density = total mass/length = 0.72 g/L

Substituting and solving for L, we get:

L = (1/2) * sqrt(Tension/linear density) / f

L = (1/2) * sqrt((18130 N)/((0.72 g/L)*(0.001 kg/g))) / 1280 Hz

L = 0.0615 m = 6.15 cm

Therefore, the length of the wire is 6.15 cm, which corresponds to choice (B).

A Length of Piano Wire Is Used to Hang a Mass