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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Sound Waves

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Sound Waves

A source of sound operates at 2.0 kHz and 20 W , radiating sound...

A source of sound operates at 2.0 kHz2.0 \text{ kHz} and 20 W20 \text{ W}, radiating sound uniformly in all directions. Given that the speed of sound in air is 340 m s−1340 \text{ m s}^{-1} and the density of air is 1.2 kg m−31.2 \text{ kg m}^{-3}, what is the intensity at a distance of 6.0 m6.0 \text{ m} from the source?

Options

  1. A11 mW m−211 \text{ mW m}^{-2}
  2. B88 mW m−288 \text{ mW m}^{-2}
  3. C22 mW m−222 \text{ mW m}^{-2}
  4. D44 mW m−244 \text{ mW m}^{-2}

Correct answer

D. 44 mW m−244 \text{ mW m}^{-2}

Step-by-step solution

The intensity of sound at a distance rr from a point source radiating uniformly in all directions is given by the power divided by the surface area of a sphere of radius rr.

I=P4πr2I = \dfrac{P}{4 \pi r^2}

Given:
Power of the source, P=20 WP = 20 \text{ W}
Distance, r=6.0 mr = 6.0 \text{ m}

Substituting the values into the formula:

I=204π(6.0)2I = \dfrac{20}{4 \pi (6.0)^2}

I=204π×36I = \dfrac{20}{4 \pi \times 36}

I=536π W m−2I = \dfrac{5}{36 \pi} \text{ W m}^{-2}

Using π≈3.14\pi \approx 3.14:

I≈5113.04 W m−2I \approx \dfrac{5}{113.04} \text{ W m}^{-2}

I≈0.0442 W m−2I \approx 0.0442 \text{ W m}^{-2}

I≈44 mW m−2I \approx 44 \text{ mW m}^{-2}

The frequency, speed of sound, and density of air are extra information not required for this calculation.
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