Question

$5beats/second$ are heard when a tuning fork is sounded with sonometer wire under tension, when the length of the sonometer wire is either $0.95m$ or $1m$. The frequency of the fork will be:

• A. $195Hz$
• B. $150Hz$
• C. $300Hz$
• D. $251Hz$

Answer 1

The correct option is A $195Hz$

When length is 0.95m

$v_1=\frac{v}{2\times 0.95}=\frac{v}{1.9}$

When length is 1m

$v_2=\frac{v}{2\times 1}=\frac{v}{2}$

$v_1-v=5v-v_2=5$

$v_1-v_2=10$

$\frac{v}{1.9}-\frac{v}{2}=10$

$\frac{0.1v}{3.8}=10$

$v=380m/s$

So, $v_1=200Hz,v_2=190Hz$

Then,

$v=195Hz$