Question

quesssssss@sssssssssssssssssssssss

Answer 1

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Answer 2

Let the Length of wire is L 
Length is increased by 2 % then number of beats heard per second is 5 
Means n₁ - n₂ = 5sec⁻¹ or, 5Hz -----(1)
Here n₁ and n₂ are the frequencies of intial and final. 

we know, n = \frac{1}{2l}\sqrt{\frac{T}{m}}2l1​mT​​ , here n is frequency , l is the length of wire , m is the mass per unit length and T is the tension in string.
so, here it is clear that frequency is inversely proportional to length of wire.
∴n₁l₁ = n₂l₂ 
n₁L = n₂1.02L { wire is increased by 2%, so L₂ = 1.02L}
50n₁ = 51n₂
n₂ = 50/51n₁ ----------(2)

from equations (1) and (2) 
n₁ - 50/51n₁ = 5 
⇒(51 - 50)/51 n₁ = 5 
⇒ 1/51 n₁ = 5 
⇒n₁ = 51 × 5 Hz = 255Hz 

Hence , frequency of turning fork is 255Hz

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