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Questions and Answers
What is the general form of a wave?
What is the general form of a wave?
y = Asin(wt - kn)
What is the relationship between particle velocity (Vp) and wave velocity (Vw)?
What is the relationship between particle velocity (Vp) and wave velocity (Vw)?
Vp = -Vw (slope)
Write the differential form of the simple harmonic wave (SHW).
Write the differential form of the simple harmonic wave (SHW).
d²y/dt² - Vw² d²y/dx² = 0
What is the formula for the power of a wave?
What is the formula for the power of a wave?
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What is the formula for the intensity of a wave in terms of amplitude and angular frequency?
What is the formula for the intensity of a wave in terms of amplitude and angular frequency?
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What is the formula for the intensity of a wave in terms of the wave's power and area?
What is the formula for the intensity of a wave in terms of the wave's power and area?
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What is the formula for the speed of a transverse wave on a stretched string?
What is the formula for the speed of a transverse wave on a stretched string?
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What is the formula for the bulk modulus of a medium?
What is the formula for the bulk modulus of a medium?
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What is Newton's formula for the speed of sound in a medium?
What is Newton's formula for the speed of sound in a medium?
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What is the Laplace formula for the speed of sound in a gas?
What is the Laplace formula for the speed of sound in a gas?
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What is the relationship between the speed of sound in a medium and the speed of a particle in the medium?
What is the relationship between the speed of sound in a medium and the speed of a particle in the medium?
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What is the formula for the change in pressure (ΔPo) due to a wave?
What is the formula for the change in pressure (ΔPo) due to a wave?
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What is the formula for the change in density (Δρ) due to a wave?
What is the formula for the change in density (Δρ) due to a wave?
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What is the formula for the change in pressure (ΔP) due to a wave in terms of amplitude and phase?
What is the formula for the change in pressure (ΔP) due to a wave in terms of amplitude and phase?
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What is the formula for the change in pressure (ΔP) in terms of the change in density (Δρ)?
What is the formula for the change in pressure (ΔP) in terms of the change in density (Δρ)?
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What is the formula for the resultant intensity (JR) of two waves?
What is the formula for the resultant intensity (JR) of two waves?
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What is the formula for the resultant amplitude (AR) and intensity (IR) of two waves with equal amplitudes?
What is the formula for the resultant amplitude (AR) and intensity (IR) of two waves with equal amplitudes?
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Study Notes
Waves
- General form of a wave: y = A sin(ωt - kx)
- Wave Propagation: Describes how a wave propagates through a medium, typically expressed as a function of space and time.
- Wave speed (v): The speed at which a wave travels through a medium, often determined by the medium's properties.
- The speed of a transverse wave on a stretched string is given by v = √(T/μ), where T is the tension in the string and μ is the linear mass density.
- Differential form of a Simple Harmonic Wave (SHW): d²y/dt² = -ω²y
- Intensity (I): A measure of the power per unit area carried by a wave.
- Relation between particle velocity (vp) and wave velocity (vw): vp = -ωA cos(ωt - kx).
- Relationship between wave number (k) and wavelength (λ): k = 2π/λ
- Relationship between angular frequency (ω) and frequency (f): ω = 2πf
- Laplace's formula: Vs = √(γRT/M)
Types of Waves
- Spherical waves: Represent waves that spread out in three dimensions from a point source. Described by y = A₀ sin(ωt - kr).
- Cylindrical waves: Radiate outward from a line source, commonly encountered in sound propagation. y is proportional to 1/√r.
Interference
- Constructive interference: Occurs when two waves combine to produce a wave with a larger amplitude.
- Destructive interference: Occurs when two waves combine to produce a wave with a smaller amplitude, potentially zero amplitude.
- Intensity (I) in constructive interference: I = I₁ + I₂ + 2√(I₁I₂)cosθ (for two waves).
- Intensity (I) in destructive interference: I = I₁ + I₂ − 2√(I₁I₂)cosθ (for two waves).
- Constructive/destructive interference depends on the phase difference.
- Phase difference expressed as Δφ relates to the phase difference
Standing Waves
- Reflection of waves at a fixed end yi = - A sin(wt - kx).
- Reflection of waves at a free end yr = A sin(wt + kx)
Standing Waves and Boundary Conditions
- Boundary conditions: Rules that govern the behavior and values at the boundaries of a medium.
- Wave amplitude at boundary depends on the boundary condition (fixed or free)
- Reflected wave at fixed end: yi = -AR sin(wt + kx) (inverted when reflected)
- Reflected wave at free end: yi = AR sin(wt - kx) (no inversion when reflected)
Other Topics (in snippets)
- Relative and Absolute loudness: Measured in decibels (dB), relative is a comparison to a reference level, absolute is the actual intensity.
- Amplitude: The maximum displacement from the equilibrium position.
- Wavelength (λ): The distance between corresponding points on two consecutive waves.
- Frequency (f): The number of waves passing a point per unit time.
- Period (T): The time taken for one complete cycle of a wave.
- Wave number (k): 2π/λ.
- Angular frequency (ω): 2πf.
- Reflection coefficients and transmission coefficients used when wave is reflected or transferred at boundaries.
- Newton's Formula: A formula relating wave speed to tension and linear mass density
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