Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
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 pressure amplitude at a distance of 6.0 m6.0 \text{ m} from the source?

Options

  1. A12 Pa12 \text{ Pa}
  2. B6.0 Pa6.0 \text{ Pa}
  3. C3.0 Pa3.0 \text{ Pa}
  4. D8.5 Pa8.5 \text{ Pa}

Correct answer

B. 6.0 Pa6.0 \text{ Pa}

Step-by-step solution

Intensity of sound at a distance rr from a point source is given by

I=P4πr2I = \dfrac{P}{4 \pi r^2}

The relation between intensity and pressure amplitude pmp_m is

I=pm22ρvI = \dfrac{p_m^2}{2 \rho v}

Equating the two expressions for intensity:

P4πr2=pm22ρv\dfrac{P}{4 \pi r^2} = \dfrac{p_m^2}{2 \rho v}

pm=Pρv2πr2p_m = \sqrt{\dfrac{P \rho v}{2 \pi r^2}}

Substituting the given values P=20 WP = 20 \text{ W}, ρ=1.2 kg m−3\rho = 1.2 \text{ kg m}^{-3}, v=340 m s−1v = 340 \text{ m s}^{-1}, and r=6.0 mr = 6.0 \text{ m}:

pm=20×1.2×3402π×(6.0)2p_m = \sqrt{\dfrac{20 \times 1.2 \times 340}{2 \pi \times (6.0)^2}}

pm=816072πp_m = \sqrt{\dfrac{8160}{72 \pi}}

pm=3403πp_m = \sqrt{\dfrac{340}{3 \pi}}

Using π≈3.14\pi \approx 3.14:

pm≈36.07≈6.0 Pap_m \approx \sqrt{36.07} \approx 6.0 \text{ Pa}
Practice Sound Waves on Quantrex Academy →

More from Sound Waves

A steel tube of length 1.00 m is struck at one end. A person with an ear close to the… Concepts Of Physics MCQ Edition [Volume 1]A man stands in front of a large wall at a distance of 50.0 m and claps his hands at… Concepts Of Physics MCQ Edition [Volume 1]Determine the minimum and maximum wavelengths of sound in water within the audible range… Concepts Of Physics MCQ Edition [Volume 1]A person is able to hear sound waves within the frequency range of 20 Hz to 20 kHz .… Concepts Of Physics MCQ Edition [Volume 1]Sound is primarily transmitted in the forward direction when its wavelength is… Concepts Of Physics MCQ Edition [Volume 1]Sound waves from a loudspeaker propagate nearly uniformly in all directions when the… Concepts Of Physics MCQ Edition [Volume 1]During a spiritual gathering, the devotees chant HARE-RAM HARE-RAM. The sound is… Concepts Of Physics MCQ Edition [Volume 1]A travelling sound wave is described by the equation y = 6.0 (600 t - 1.8 x) , with y… Concepts Of Physics MCQ Edition [Volume 1] Full Sound Waves list All Concepts Of Physics MCQ Edition [Volume 1] PYQs