When a sonometer wire and a tuning fork are sounded together , they produce $5$ beats per second ,when the length of the wire is either $95 c m$ or $100 c m$ .Determine the frequency of fork ?

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Solution

Tunning fork are sounded together $5$ beats per second are produced or $5 H Z .$
let frequency of fork $= V$
then $,$ probably frequencies of tunning fork due to beats formation are $(V + 5) H Z$ and $(V - 5) H Z .$
we know $,$
Frequency is inversely proportional to length of wire
$∴ \frac{(V + 5)}{(V - 5)} = \frac{100}{95}$
$\Rightarrow 95 (V + 5) = 100 (V - 5)$
$\Rightarrow 19 (V + 5) = 20 (V - 5)$
$\Rightarrow 19 V + 95 = 20 V - 100$
$\Rightarrow 95 + 100 = 20 V - 19 V$
$\Rightarrow 195 = V$
Hence, frequency of fork $= 195 H Z .$

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When a sonometer wire and a tuning fork are sounded together , they produce 5 beats per second ,when the length of the wire is either 95 cm or 100 cm .Determine the frequency of fork ?

When a sonometer wire and a tuning fork are sounded together , they produce $5$ beats per second ,when the length of the wire is either $95 c m$ or $100 c m$ .Determine the frequency of fork ?