Question

The fundamental frequency of a sonometre wire is
n. If its radius is doubled and its tension becomes
half, the material of the wire remains same, the
new fundamental frequency will be ​

Answer 1

Answer:

Explanation:

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