Sound Intensity and Decibels – Rankers Physics

Sound Wave and its Characteristics: Practice Problem & Solution

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

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Sound Wave and its Characteristics. Understanding the underlying formula is key to arriving at the correct answer below:

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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