In a sonometer experiment the bridges are separted by a fixed distance the wire which is slightly elastic emits a tone of frequency n when held by tension T If the tension is increased to 4T the tone emitted by the wire will be of frequency

Options

A. n
B. 2n
C. slightly greater than 2n
D. slightly less than 2n

Answer

b

Explanation

Frequency of wave produced in the wire
`n=1/(2l)xxsqrt(T/mu)` …(i)
wher, `l=` length of the wire
`mu=` mass per unit length
`T =` tension in the wire
Frequency produced when tension changes to T'

`n'=1/(2l) xx sqrt((T')/mu)`
`n' = 1/(2l) xx sqrt((4T)/mu) ` ...(ii)
On dividing Eq. (i) and (ii), we get
`n/(n') = sqrt(1/4) =1/2 rArr n' = 2n`