Question

In the sonometer experiment, a student
obtains 16 cm as the resonance length
when tension in sonometer wire is
half 1/2kg.
What would be the resonance length if
tension is increased by1.5 kg? (resonance
length is length of wire in fundamental
mode)
(A) 16 cm
(B) 32 cm
(C) 8 cm
(D) 64 cm​

Answer 1

I think answer of this question must be 16cm

Answer 2

If the tension in the sonometer wire is increased by 1.5 kg, the resonance length will be 32 cm

Explanation:

The frequency of vibration is given by

$\boxed{f=\frac{1}{2l}\sqrt{\frac{T}{m}}}$

Where, T is the tension and l is the length and m is mass per unit length

Thus, we can say that

$\frac{\sqrt{T_1}}{l_1}=\frac{\sqrt{T_2}}{l_2}$

Given,

$T_1=0.5$ kg

$l=16$ cm

$T_2=0.5+1.5=2$ kg

$l_2=?$

Thus,

$\frac{\sqrt{0.5}}{16}=\frac{\sqrt{2}}{l_2}$

$\implies \frac{0.5}{16^2}=\frac{2}{l_2^2}$

$\implies l_2^2=\frac{2\times 16\times 16}{0.5}$

$\implies l_2^2=2\times2\times 16\times 16$

$\implies l_2=2\times 16=32$ cm

Hope this answer is helpful.

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