TS EAMCET · Physics · Units and Dimensions

A message signal of frequency $f_{m}$ is used to modulate a carrier of frequency $f_{c} .$ If the side bands are $f_{1}$ and $f_{2}$ then the ratio $\frac{f_{c}}{f_{m}}$ is

A $|\frac{f_{1} + f_{2}}{f_{2} - f_{1}}|$
B $\frac{{(f_{1} + f_{2})}^{2}}{f_{1} f_{2}}$
C $|\frac{f_{1} - f_{2}}{f_{2} + f_{1}}|$
D $\frac{f_{1} f_{2}}{{(f_{1} + f_{2})}^{2}}$

Verified Solution

Answer & Solution

Correct Answer

(A) $|\frac{f_{1} + f_{2}}{f_{2} - f_{1}}|$

Step-by-step Solution

Detailed explanation

The frequency of message signal is always less than carrier frequency and the frequency of the message signal is, fm=f1-f2 and the frequency of carrier signal is, fm=f1+f2, so the value of, fcfm=f1+f2f1-f2.

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 message signal of frequency fm is used to modulate a carrier of frequency fc. If the side bands are f1 and f2 then the ratio fcfm is

Step-by-step Solution

A message signal of frequency $f_{m}$ is used to modulate a carrier of frequency $f_{c} .$ If the side bands are $f_{1}$ and $f_{2}$ then the ratio $\frac{f_{c}}{f_{m}}$ is