Question

Two stretched wires are in unison. If the tension in one of the wire is increased by $1\%$ $3$beats are produced in $2$s. The initial frequency of each wire is?

• A. $150$Hz
• B. $200$Hz
• C. $300$Hz
• D. $450$Hz

Answer 1

The correct option is C $300$Hz

$n_1=k\sqrt{T},n_2=k\sqrt{1.01T}$
$\because n_2-n_1=\frac{3}{2}$
$k(\sqrt{1.01T}-\sqrt{T})=1.5$
$k\sqrt{T}\left[\right(1+0.01{)}^{1/2}-1]=1.5$
$k\sqrt{T}[1+\frac{1}{2}\times 0.01-1]=1.5$
$k\sqrt{T}=\frac{1.5\times 2}{0.01}$
$\therefore n_1=k\sqrt{T}$
$=\frac{1.5\times 2}{0.01}$
$=300$Hz.
We know that beat frequency is the difference of two frequencies, i.e., $f_1-f_2$.