Question

Two instruments having stretched strings are being played in unison. When the tension of one of the instruments is increased by $1\%, 3$ beats are produced in $2\,s$ . The initial frequency of vibration of each wire is:

• A. 300 Hz
• B. 500 Hz
• C. 1000 Hz
• D. 400 Hz

Answer 1

Answer: (A)

300 Hz

Answer 2

Initial frequency of vibration
$v \propto \sqrt{T}$
When the tension in one of the instruments is increased by $1 \%$, then
$v \propto \sqrt{1+\frac{1}{100}}$
$\therefore \frac{v^{'}}{v}=\left(1+\frac{1}{100}\right)^{1 / 2}$
$=1+\frac{1}{200}$
or $\frac{v^{'}-v}{v}=\frac{1}{200}$
or $\frac{3}{2 v}=\frac{1}{200}$
or $v =300\, Hz$