Sound Intensity and Decibels – Rankers Physics
Topic: Waves
Subtopic: Sound Wave and its Characteristics

Sound Intensity and Decibels

Assertion (A): A (80 \text{ dB}) sound has twice the intensity of a \(40 \text{ dB}\) sound.
Reason (R): Loudness of a sound of a certain intensity ('I') is defined as \(L = 10 log_{10} left(frac{I}{I_0}right)\).
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

Assertion (A) is false. An 80  dB sound has an intensity \(10^4\) times greater than a \(40 \text{ dB}\) sound, not twice. Reason (R) is true as it correctly defines loudness in decibels.


Since (A) is false and (R) is true, and the option for 'A is false, R is true' is not provided, option (4) is selected as it states (A) is false.

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