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  4. A tuning fork vibrating with a sonometer wire of length 20 cm produces 5 beats per second. The heat frequency does not change if the length of the wire is change to 21 cm. The frequency of the tuning fork must be

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Q. A tuning fork vibrating with a sonometer wire of length 20 cm produces 5 beats per second. The heat frequency does not change if the length of the wire is change to 21 cm. The frequency of the tuning fork must be

Waves

Solution:

Fundamental frequency is:
$n =1 / 2 l \sqrt{ T / m }$
$n 1/l$
assume for $20 cm$ frequency is $n 1$ and for $21 cm$ frequency is $n 2$ So
$n 1 / n 2=21 / 20$
then $n 1=21 \times$ and $n 2=20 x$
Let frequency nf for producing 5 beats so $n 1> nf > n 2$ So $n 1-n f=5$
$21 x-n f=5$
And $n f-n 2=5$
$n f-20 x=5$
from $(1)$ ans $(2)$ we get $x=205 h z$