AP EAMCET · PHYSICS · Waves and Sound

A source is stationary and the observer is in motion along a line joining the source and the observer. If the frequency heard by the observer is $1 %$ higher than the true frequency, the ratio of velocity of the observer and that of sound in air is:

A $1 : 100$
B $2 : 100$
C $3 : 100$
D $1 : 10$

Verified Solution

Answer & Solution

Correct Answer

(A) $1 : 100$

Step-by-step Solution

Detailed explanation

As source is stationary and the observer is moving with velocity vo Let velocity of sound v Observed frequency f in Doppler effect is given by f=v+vovfo Here f=1.01fo(Given) ⇒1.01fo=v+vovfo⇒101100=v+vov⇒vov=1100

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 source is stationary and the observer is in motion along a line joining the source and the observer. If the frequency heard by the observer is 1% higher than the true frequency, the ratio of velocity of the observer and that of sound in air is:

Step-by-step Solution

A source is stationary and the observer is in motion along a line joining the source and the observer. If the frequency heard by the observer is $1 %$ higher than the true frequency, the ratio of velocity of the observer and that of sound in air is: