A sonometer wire is 31 cm long is resonance with a tuning fork of frequency n.if the length is increased by 1 cm and it is vibrated with the same tuning fork,then 8 beats/ sec are heard.the frequency of the tuning fork is
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Given :
The length of sonometer wire = 31cm
Change in length = 1cm
Number of beats produced = 6 beats/sec
To Find :
The frequency of tuning fork = ?
Solution :
- We know the relation
No of beats produced = Difference in frequencies
8 = n₂ - n₁ …………[1]
- Frequency of wire is inversly proportional to length
(n₁/ n₂) = (l₂ / l₁)
(n₁/ n₂) = (l + Δl) / l
(n₁/ n₂) = (32 / 31)
n₂ = (32 / 31)n₁
- By substituting in equation (1) we get
(32 / 31)n₁ - n₁ = 8
(1/31) n₁ = 8
n₁ = 31× 8
n₁ = 248Hz
The frequency of tuning fork is 248Hz
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