Sound Waves: Relating Amplitude, Power and Intensity
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My LO addresses the relationship between displacement amplitude, power and intensity of sound waves. I made a PowerPoint with a couple of problems that shows and works with this relationship to further understand it.
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Lecture 07 sound waves. speed of sound. intensity.
1) Sound waves propagate as periodic longitudinal oscillations of particles in a medium, causing oscillations in pressure and density around the equilibrium values.
2) The speed of sound in a medium depends on its bulk modulus and density, following the equation v = √(B/ρ).
3) Sound intensity decreases with the square of the distance from the source, following the inverse square law. It can be calculated from the sound pressure or particle displacement using equations provided.
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This document discusses sound waves, power, intensity, and how they relate to distance from a sound source. It provides equations for power and intensity of sound waves. Power is the rate at which energy is delivered, while intensity is the power delivered per unit area. Intensity is inversely proportional to the square of the distance from an isotropic (uniformly radiating) source. The document includes a sample problem asking how the amplitude of sound waves observed by a person would change if the distance from the speaker doubled. The solution is that the amplitude would halve, since intensity, and thus amplitude, is inversely proportional to the square of the distance.
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PRESENTATION LAYOUT
Concept of Polarization
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Methods of achieving Polarization
Applications of Polarization
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Transforming unpolarized light into polarized light
Restriction of electric field vector E in a particular plane so that vibration occurs in a single plane
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Longitudinal waves can’t be polarized; direction of their oscillation is along the direction of propagation.............
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Sound Waves: Relating Amplitude, Power and Intensity
- 1. Sound waves: Relating displacement amplitude, power and intensity Alyssa Hui Phys 101 201 LO4
- 2. • Power (P) is the rate at which the energy is transferred by a wave, with units of J/s • Intensity is the power delivered per unit area, giving units of W/m2 • Intensity is also determined by the density of the medium, wave speed, angular frequency and the displacement amplitude (sm) Concepts
- 3. • When we double the power produced by a source, by what factor does the displacement amplitude of the resultant wave change? Problem 1 cr: desmos.com
- 4. •I = P/A •I = ½ ρvω2sm 2 Relevant Equations
- 5. • Can you find the relationship between sm and P? Hint
- 6. • Setting the two equations for intensity equal to each other, we can solve for sm, ½ ρvω2sm 2 = P/A sm = (2𝑃/(𝐴𝜌𝑣𝜔2)) • If P is doubled, sm = (2 ∗ (2𝑃)) the displacement amplitude of the resultant wave increases by approx. 1.4. Solution
- 7. • The equation sm = (2𝑃/(𝐴𝜌𝑣𝜔2)) can be used to determine relationships between other properties in a sound wave, such as in the following problem. Note
- 8. • A person is standing beside a speaker as it plays a 10,000 Hz tone. The sound waves travel away from the speaker uniformly in all directions. If the distance from the speaker doubles, then the amplitude of the waves that the person observes: Problem 2
- 9. • (From previous problem) sm = (2𝑃/(𝐴𝜌𝑣𝜔2)) Relevant Equation
- 10. •What area does power radiating isotropically cover? Hint
- 11. • Radiating isotropically means waves will travel uniformly in all directions; therefore power is radiated over A = 4πr2, sm = (2𝑃/(4πr2 ∗ 𝜌𝑣𝜔2)) • With distance doubled, radius r is doubled, sm = (1/ 2𝑟 2) and the amplitude of the waves is halved. Solution