A piano wire having a diameter of `0.90 mm` is replaced by another wire of the same material but with a diameter of `0.93 mm`.If the tension of the wire is kept the same , then the percentage change in the frequency of the fundamental tone is

Options

A. 0.03
B. 0.003
C. `+3.2%`
D. `-3.26%`

Answer

D

Explanation

`d_1=0.90mm, d_2 = 0.93 mm`
`n_1 prop 1/d_1 " and " n_2 prop 1/d_2`
`(n_2)/(n_1) - 1= (d_1)/(d_2) -1 = 90/93-1`
`therefore (n_2-n_1)/(n_1) xx100 = ((90-93)/(93)) 100 = (-3)/(93) xx100`
`(n_2-n_1)/(n_1)% = (-1)/(31) xx100 = -0.0326xx100`
=-3.26%