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

Question

What is the fractional change in tension necessary in a sonometer of fixed length to produce a note one octave lower than before? (A) (1/4) (B) (1/2) (C) (2/3) (D) (3/4)

Tardigrade Admin · Accepted Answer

n =(1/2l) √( T'/ m ) ( n /2)=(1/2l) √( T'/ m ) by (i) (ii) ( T'/ T )=(1/4) Subtract both side from 1 -1-(T'/T)=1-(1/4) ( T - T'/ T )=(3/4)

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

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{2}{3}$

$\frac{3}{4}$

$n = \frac{1}{2 l} \frac{T ^{'}}{m}$
$\frac{n}{2} = \frac{1}{2 l} \frac{T ^{'}}{m}$
by (i) $&$ (ii)
$\frac{T ^{'}}{T} = \frac{1}{4}$
Subtract both side from 1
$- 1 - \frac{T ^{'}}{T} = 1 - \frac{1}{4}$
$\frac{T - T ^{'}}{T} = \frac{3}{4}$