A piano wire 50 cm long has a total mass of 10 g and its stretched with a tension of 800 N. Find the frequency of the wire when it sounds its third overtone note.

A. 800 Hz

B. 600 Hz

C. 400 Hz

D. 200 Hz

Correct Option: Answer is D

The frequency (f) of a stretched string can be calculated using the formula:

F =1/(2L ) âˆš(T/u)

where:

L is the length of the string,

T is the tension in the string,

Î¼ is the linear mass density of the string.

The linear mass density (Î¼) is given by the formula:

Î¼ = m/(L )

where:

m is the mass of the string,

L is the length of the string.

Given:

L=50â€‰cm=0.5â€‰m

T=800â€‰N

m=10â€‰g=0.01â€‰kg

First, calculate the linear mass density:

u= 0.01/(0.5m ) = 0.02kg/m

Now, substitute the values into the frequency formula:

F =1/(2 x 0.5 ) âˆš40000

f=200â€‰Hz