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. ` + 3 %`
B. `+ 3.2 %`
C. `- 3.2 %`
D. `- 3%`

Answer

C

Explanation

`v = (1)/(Dl) sqrt((T)/(pi d)) or v prop (1)/(D)`
Now , `((v')/(v) - 1) xx 100 = (30/31) - 1) xx 100`
` = - (100)/(31) = - 3.2`.