TS EAMCET · Physics · Waves and Sound

Two waves of amplitudes $A_{1}$ and $A_{2}$ respectively are superimposed. The ratio between the maximum and minimum intensities of the resultant waves is $9 : 4$ . The value of $\frac{A_{2}}{A_{1}}$ is [Assume $A_{1} > A_{2}$ ]

A $0.66$
B $0.20$
C $0.75$
D $0.44$

Verified Solution

Answer & Solution

Correct Answer

(B) $0.20$

Step-by-step Solution

Detailed explanation

Intensity of a wave I is related with the amplitude of a wave as, I∝A2. The ratio of maximum to minimum intensity will be, ImaxImin=A1+A2A1-A22⇒A1+A2A1-A2=32⇒A2A1=15=0.2

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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Two waves of amplitudes A1 and A2 respectively are superimposed. The ratio between the maximum and minimum intensities of the resultant waves is 9:4. The value of A2 A1 is [Assume A1>A2]

Step-by-step Solution

Two waves of amplitudes $A_{1}$ and $A_{2}$ respectively are superimposed. The ratio between the maximum and minimum intensities of the resultant waves is $9 : 4$ . The value of $\frac{A_{2}}{A_{1}}$ is [Assume $A_{1} > A_{2}$ ]