MHT CET · Physics · Waves and Sound

The fundamental frequency of sonometer wire increases by 9 Hz, if its tension is increased by $69 %$ , keeping the length constant. The frequency of the wire is

A 42 Hz
B 24 Hz
C 30 Hz
D 36 Hz

Verified Solution

Answer & Solution

Correct Answer

(C) 30 Hz

Step-by-step Solution

Detailed explanation

We know that, frequency of vibration of a stretched string is given by

v = \frac{1}{2 l} \sqrt{\frac{T}{m}}

where,

T

= tension in string

m

= mass /length
and

l

= length of string.
New frequency,

v^{'} = v + 9 = \frac{1}{2 l} \sqrt{\frac{T + (69 / 100) T}{m}}

\Rightarrow \frac{v}{v^{'}} = \sqrt{\frac{\frac{T}{169}}{100} T} \Rightarrow \frac{v}{v + 9} = \sqrt{\frac{100}{169}} = \frac{10}{13}

\Rightarrow 13 v = 10 v + 90

v = 30 H z

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The fundamental frequency of sonometer wire increases by 9 Hz, if its tension is increased by 69% , keeping the length constant. The frequency of the wire is

Step-by-step Solution

The fundamental frequency of sonometer wire increases by 9 Hz, if its tension is increased by $69 %$ , keeping the length constant. The frequency of the wire is