AP EAMCET · PHYSICS · Waves and Sound

If the length of a stretched string is shortened by $x %$ and the tension is increased by $44 %$ then the ratio of the initial and final fundamental frequencies is $1 : 2$ , the value of $' x'$ is

A $20$
B $30$
C $40$
D $60$

Verified Solution

Answer & Solution

Correct Answer

(C) $40$

Step-by-step Solution

Detailed explanation

Recall the formula of fundamental frequency in terms of tension and mass per unit length, f=12lTμ it means, f1f2=12l1T1μf=12l2T2μ=l2l1×T1T2 Put given data, 12=l1-x100l×TT1+44100⇒12=100-x10×112⇒60=100-x⇒x=40

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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If the length of a stretched string is shortened by x% and the tension is increased by 44% then the ratio of the initial and final fundamental frequencies is 1:2, the value of 'x' is

Step-by-step Solution

If the length of a stretched string is shortened by $x %$ and the tension is increased by $44 %$ then the ratio of the initial and final fundamental frequencies is $1 : 2$ , the value of $' x'$ is