Beat Frequencies and Superposition – Rankers Physics
Topic: Waves
Subtopic: Sound Wave and its Characteristics

Beat Frequencies and Superposition

Assertion (A): When two tuning fork of frequency \(256 \text{ Hz}\) and \(324 \text{ Hz}\) are vibrating together. Beats will not be heard.
Reason (R): Superposition of sound waves is possible for all frequencies of sound.
 
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution:

The beat frequency is \(|256 - 324| = 68 \text{ Hz}\) . Since this is much greater than \(10 \text{ Hz}\) , distinct beats cannot be heard. Thus, (A) is true. The principle of superposition holds for all sound waves irrespective of their frequency, so (R) is true. However, (R) does not explain (A).

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