The power output of an audio system is 18 W. For a person to notice an increase in the output (loudness or sound intensity) of the system, what must the output power be increased to ?

Solution (By Examveda Team)

Correct Answer: Option C — 68 W

Explanation:
Human hearing perceives loudness on a logarithmic scale. Therefore, a noticeable increase in sound output requires a significant increase in the actual power of the audio system.

The change in sound power level is calculated using:

Change in dB = 10 × log₁₀(P₂/P₁)

Given:
Initial power, P₁ = 18 W
New power, P₂ = 68 W

Therefore:
Change in dB = 10 × log₁₀(68/18)
= 10 × log₁₀(3.78)
≈ 10 × 0.577
≈ 5.77 dB

A 3 dB increase corresponds to approximately a doubling of sound power. Since increasing the power from 18 W to 68 W produces an increase of approximately 5.77 dB, the change in output would be clearly noticeable.

Option A — 2 W: This is a decrease in power, so the sound output would decrease.

Option B — 6 W: This is also a decrease in power, so the sound would become quieter.

Option C — 68 W: This increases the power from 18 W to 68 W, producing approximately a 5.77 dB increase. Hence, this is the correct option.

Option D — None of the above: Incorrect because 68 W satisfies the requirement in the context of the question.

Remember for Exams: 3 dB increase ≈ 2× power. The relationship between power and decibels is ΔdB = 10 log₁₀(P₂/P₁).

Final Answer: Option C — 68 W