The fundamental frequency of a sonometer wire is n if it's length
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Sonometer.
Radius = r. Density = d. Tension in the wire = T.
μ = mass/ length = d * pi* r^2
Velocity = sqrt(T/μ).
Fundamental tone Wavelength = lambda = 2* L.
Frequency n = 1/(2L) * sqrt (T/(pi *d*r^2))
If L, T and r are 3 times then:
New n = 1/(2*3*L)* sqrt(3*T/(pi*3d*9r^2))
= 1/9 * old n.
Frequency reduced to 1/9 times.
Radius = r. Density = d. Tension in the wire = T.
μ = mass/ length = d * pi* r^2
Velocity = sqrt(T/μ).
Fundamental tone Wavelength = lambda = 2* L.
Frequency n = 1/(2L) * sqrt (T/(pi *d*r^2))
If L, T and r are 3 times then:
New n = 1/(2*3*L)* sqrt(3*T/(pi*3d*9r^2))
= 1/9 * old n.
Frequency reduced to 1/9 times.
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