Question

What is the fractional change in tension necessary in a sonometer wire of fixed length to produce a note one octave lower than before

Answer 1

The fractional change in tension will be 3/4

Explanation :

we know that note  is given by

n = $\frac{1}{2l} \sqrt{T/m}$

where T = tension

m = mass

l = length

let T' be the new tension for producing a note one octave lower than before;

hence,

n/2 = $\frac{1}{2l} \sqrt{T'/m}$

Dividing both the equation we get

2 = √(T/T')

=> T/T' = 4

=> T' = T/4

hence change in tension

= T - T'

= T - T/4

= 3T/4

hence the fractional change in tension will be 3/4