Podcast
Questions and Answers
What is the general form of a wave represented by the equation?
What is the general form of a wave represented by the equation?
What is the formula for calculating the speed of a transverse wave on a stretched string?
What is the formula for calculating the speed of a transverse wave on a stretched string?
What happens to wave amplitude when moving from a rarer to a denser medium?
What happens to wave amplitude when moving from a rarer to a denser medium?
In constructive interference, how is the resultant amplitude (AR) calculated when A₁ = A₂?
In constructive interference, how is the resultant amplitude (AR) calculated when A₁ = A₂?
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What is the equation for power in wave mechanics?
What is the equation for power in wave mechanics?
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In terms of intensity, what does the formula Imax = (√I₁ + √I₂)² calculate?
In terms of intensity, what does the formula Imax = (√I₁ + √I₂)² calculate?
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Which formula describes the phase difference in wave propagation?
Which formula describes the phase difference in wave propagation?
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What is the term for the coefficient that measures the amplitude of the reflected wave?
What is the term for the coefficient that measures the amplitude of the reflected wave?
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Study Notes
Waves
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General form of a wave: y = A sin(ωt – kx) where A is amplitude, ω is angular frequency, t is time, k is wave number, and x is position.
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Wave Number (k): k = 2π/λ, where λ is wavelength.
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Angular Frequency (ω): ω = 2πf, where f is frequency.
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Relationship between particle velocity (vp) and wave velocity (vw): vp = -vw(slope)
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Differential form of a simple harmonic wave (SHW): d²y/dt² = -ω²y
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Intensity (I) of a wave: I = (1/2)μω²A²
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Wave speed on a stretched string: v = √(T/μ) where T is tension and μ is linear mass density.
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Newton's formula for the speed of sound: v = √(γP/ρ), where γ is adiabatic index, P is pressure, and ρ is density
Other Wave Concepts
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Laplace formula: vs = √γRT/M
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Relative and Absolute loudness: L(dB) = 10log₁₀(I/I₀), where I is intensity and I₀ is a reference intensity (typically the threshold of hearing).
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Wave speed (v) and frequency (f): v = fλ
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Spherical waves: y = A₀ sin(ωt ± kx)
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Cylindrical waves: y = A₀ sin(ωt ± kx)/r
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Reflection at a fixed end: yr = -Asin(ωt + kx)
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Reflection at a free end: yr = Asin(ωt + kx)
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Constructive interference: Amplitude of reflected wave + Amplitude of transmitted wave = AR + AT
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Destructive interference: AR = (√V₂ - √V₁)/√(√V₂ + √V₁)
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Amplitude of reflected wave (AR): AR = (V₂ - V₁)/(V₂ + V₁) * A₀
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Amplitude of transmitted wave (AT) : AT = 2 * V₁/(V₁ + V₂) * A₀
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Wave Equations for Reflected & Transmitted Waves at Boundaries (Denser/Rarer Medium): Equations for wave amplitude are presented for various boundary scenarios.
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Description
Dive into the fascinating world of waves with this quiz that covers essential concepts such as wave equations, wave number, angular frequency, and intensity. Understand the mathematical relationships that describe wave behavior and explore key formulas related to wave speed and sound. Perfect for physics students looking to test their knowledge on wave mechanics!
