MHT CET · Physics · Waves and Sound

A wire having tension $225 N$ produces six beats per second when it vibrates with some tuning fork. When the tension changes to $256 N$ , it vibrates with the same fork with the number of beats remaining unchanged. The frequency of the fork will be

A $186 Hz$
B $225 Hz$
C $256 Hz$
D $280 Hz$

Verified Solution

Answer & Solution

Correct Answer

(A) $186 Hz$

Step-by-step Solution

Detailed explanation

For wire vibrating under tension, the fundamental frequency is given by

f_{1} = \frac{1}{2 L} \sqrt[]{\frac{T}{μ}}

, Where T is tension and

μ

linear mass density of string
It is given that, when it is sounded with a tuning fork of frequency

x

6

beats per second were heard

∴ (x - f) = 6

f_{1} = \frac{1}{2 L} \sqrt{\frac{225}{μ}}

f_{2} = \frac{1}{2 L} \sqrt{\frac{256}{μ}}

undefined

∴ (x + 6) = \frac{16}{15} (x - 6)

∴ 15 x + 90 = 16 x - 96

∴ x = 186 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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A wire having tension 225 N produces six beats per second when it vibrates with some tuning fork. When the tension changes to 256 N, it vibrates with the same fork with the number of beats remaining unchanged. The frequency of the fork will be

Step-by-step Solution

A wire having tension $225 N$ produces six beats per second when it vibrates with some tuning fork. When the tension changes to $256 N$ , it vibrates with the same fork with the number of beats remaining unchanged. The frequency of the fork will be