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Waves

Question

When a stretched wire and a tuning fork are sounded together, 5 beats per second are produced, when length of wire is 95 cm or 100 cm, frequency of the fork is

90 Hz

100 Hz

105 Hz

195 Hz

Solution

195 Hz

Tunning fork are sounded together 5 beats per second are produced or 5Hz

Let frequency of fork = n

Then probably frequencies of tunning fork due to beats due to beats formation are

( n + 5 ) Hz and ( n $-$ 5 ) Hz

We know

Frequency is inversely proportional to length of wire

∴ $\frac{n + 5}{n - 5} = \frac{100}{95}$

⇒ 95 ( n + 5 ) = 100 ( n $-$ 5 )

⇒ 19 ( n + 5 ) = 20 ( n $-$ 5 )

⇒ 19n + 95 = 20n $-$ 100

⇒ 95 + 100 = 20n $-$ 19n

⇒ n = 195

Hence frequency of the fork is 195 Hz