Question

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

• A. 200 Hz
• B. 210 Hz
• C. 205 Hz
• D. 215 Hz

Answer 1

Answer: (C)

Fundamental frequency is:
$n=1/2l\sqrt{T/m}$
$n1/l$
assume for $20cm$ frequency is $n1$ and for $21cm$ frequency is $n2$ So
$n1/n2=21/20$
then $n1=21\times$ and $n2=20x$
Let frequency nf for producing 5 beats so $n1>nf>n2$ So $n1-nf=5$
$21x-nf=5$
And $nf-n2=5$
$nf-20x=5$
from $(1)$ ans $(2)$ we get $x=205hz$