Waves Overview Quiz

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Questions and Answers

What happens to the water surface when a pebble is dropped in a pond?

  • The water remains still.
  • The water only rises at the point where the pebble is dropped.
  • The water flows away from the point of disturbance.
  • The water is disturbed and the disturbance propagates outward. (correct)

The cork pieces on the disturbed water surface move outward from the center of disturbance.

False (B)

What binds the constituents in a material medium?

Elastic forces

When we speak, the sound moves outward through a __________.

<p>medium</p> Signup and view all the answers

Which type of wave is characterized by particle motion perpendicular to the direction of wave propagation?

<p>Transverse wave (C)</p> Signup and view all the answers

Match the types of waves with their descriptions:

<p>Transverse wave = Particle motion is perpendicular to wave direction Longitudinal wave = Particle motion is parallel to wave direction Surface wave = Combination of transverse and longitudinal wave motion Sound wave = Traveling pressure disturbances in a medium</p> Signup and view all the answers

The principle of superposition allows two waves to intersect without altering each other's speed.

<p>True (A)</p> Signup and view all the answers

When multiple pebbles are dropped in the pond simultaneously, waves created __________.

<p>interfere</p> Signup and view all the answers

What is the equation representing the motion of a fixed phase point on the wave?

<p>kx - ωt = constant (D)</p> Signup and view all the answers

The frequency of the wave is 1.5 Hz.

<p>False (B)</p> Signup and view all the answers

What is the relationship between the period (T) and angular frequency (ω)?

<p>T = 2π/ω</p> Signup and view all the answers

The displacement at x = 30.0 cm and t = 20 s is given by y = (0.005 m) sin (80.0 × 0.3 – 3.0 × ___).

<p>20</p> Signup and view all the answers

What is the value of k in the equation kx - ωt = constant?

<p>80.0 m⁻¹ (B)</p> Signup and view all the answers

The speed of a mechanical wave is determined solely by its frequency.

<p>False (B)</p> Signup and view all the answers

What is the speed of propagation of the traveling wave described?

<p>v = λν</p> Signup and view all the answers

Match the following terms with their definitions:

<p>T = Time for one complete oscillation k = Wave number λ = Wavelength ω = Angular frequency</p> Signup and view all the answers

What is the formula for the speed of a wave on the wire?

<p>v = T / µ (B)</p> Signup and view all the answers

The dimension of tension T is [MLT–2].

<p>True (A)</p> Signup and view all the answers

What is the dimension of the mass per unit length (µ)?

<p>[ML–1]</p> Signup and view all the answers

The speed of a longitudinal wave is determined by the relationship v = _____.

<p>T / µ</p> Signup and view all the answers

What does the term φ represent in the argument of the sine function?

<p>Phase constant (C)</p> Signup and view all the answers

Match the definitions with their respective terms:

<p>Tension = Force applied along the length of a medium Bulk Modulus = Measure of a medium's resistance to uniform compression Speed of Sound = Speed at which sound propagates through a medium Longitudinal Wave = Wave where oscillation occurs in the direction of propagation</p> Signup and view all the answers

What is the undetermined constant C in the formula for the speed of a wave?

<p>1 (B)</p> Signup and view all the answers

The particle motion in water waves involves only vertical motion.

<p>False (B)</p> Signup and view all the answers

What distinguishes transverse waves from longitudinal waves in a medium?

<p>Transverse waves oscillate perpendicular to the direction of wave propagation, while longitudinal waves oscillate parallel to the direction of wave propagation.</p> Signup and view all the answers

Dimensional analysis can provide exact formulas.

<p>False (B)</p> Signup and view all the answers

The amplitude of a wave is represented by the variable ____.

<p>a</p> Signup and view all the answers

In a longitudinal wave, how do the constituents of the medium oscillate?

<p>Forward and backward in the direction of wave propagation</p> Signup and view all the answers

Match the following physical quantities to their representations in the equations:

<p>Amplitude = a Angular Frequency = ω Wave Number = k Displacement = y(x, t)</p> Signup and view all the answers

In equation $y(x, t) = A \sin(kx - \omega t) + B \cos(kx - \omega t)$, what does the term A refer to?

<p>Amplitude from sine component (A)</p> Signup and view all the answers

A wave described by the equation $y(x, t) = a \sin(kx + \omega t + φ)$ travels in the positive direction along the x-axis.

<p>False (B)</p> Signup and view all the answers

Describe how the displacement y varies with time at a fixed location x.

<p>The displacement y varies sinusoidally with time at a fixed location x.</p> Signup and view all the answers

What does the variable 'a' represent in the context of wave displacement?

<p>The amplitude of the wave (D)</p> Signup and view all the answers

The phase of a wave is constant and does not change with time.

<p>False (B)</p> Signup and view all the answers

What is the term used to describe the point of maximum negative displacement in a wave?

<p>trough</p> Signup and view all the answers

The initial phase angle is denoted by ______.

<p>φ</p> Signup and view all the answers

Which equation shows the relationship for wave displacement?

<p>y(x,t) = a sin(kx – ωt + φ) (D)</p> Signup and view all the answers

The crest of a wave is the point of maximum positive displacement.

<p>True (A)</p> Signup and view all the answers

The solid dot at the origin shows the motion of a particle at a fixed location, called a ______.

<p>constituent</p> Signup and view all the answers

What is the adiabatic bulk modulus for an ideal gas represented by?

<p>$B_{ad} = -\frac{\Delta P}{\frac{\Delta V}{V}}$ (A), $B_{ad} = \gamma P$ (B)</p> Signup and view all the answers

The notion of superposition states that wave pulses do not interact with each other when they overlap.

<p>True (A)</p> Signup and view all the answers

What is the mathematical expression for net displacement when two waves overlap?

<p>y(x,t) = y1(x,t) + y2(x,t)</p> Signup and view all the answers

The speed of sound in air at STP is approximately ______ m/s.

<p>331.3</p> Signup and view all the answers

Which parameter is represented by γ in the adiabatic bulk modulus formula?

<p>Specific heat ratio (D)</p> Signup and view all the answers

Match the terms with their definitions:

<p>Adiabatic bulk modulus = Change in pressure over volume change Laplace correction = Modification of Newton's formula for sound Principle of superposition = Net displacement of overlapping waves Speed of sound = Rate at which sound travels through a medium</p> Signup and view all the answers

What occurs to the net displacement if two wave pulses exhibit identical displacements in opposite directions?

<p>Zero displacement</p> Signup and view all the answers

The speed of sound formula includes the density of the medium.

<p>True (A)</p> Signup and view all the answers

Flashcards

Amplitude (a)

The maximum displacement of particles in a medium from their equilibrium position. It represents the peak height of a wave.

Phase (kx - ωt + φ)

The argument of the sine function in a wave equation (kx - ωt + φ). It determines the displacement of the wave at any point in space and time.

Initial Phase Angle (φ)

The phase of a wave at x = 0 and t = 0. It indicates the starting point of a wave's oscillation.

Crest

The point of maximum positive displacement in a wave. It's the 'peak' of the wave.

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Trough

The point of maximum negative displacement in a wave. It's the 'valley' of the wave.

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Wave

A disturbance that travels through a medium, transferring energy without transporting matter.

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Transverse wave

A wave in which the particles of the medium oscillate perpendicular to the direction of wave propagation. Think of a wave on a rope.

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Longitudinal wave

A wave in which the particles of the medium oscillate parallel to the direction of wave propagation. Think of a sound wave traveling through air.

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Wavelength (λ)

The distance between two consecutive crests or troughs of a wave, representing one full cycle.

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Frequency (f)

The number of complete wave cycles passing a point in one second.

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Wave speed (v)

The speed at which a wave propagates through a medium.

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Superposition of waves

The combined effect of two or more waves overlapping in a medium.

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Reflection of waves

The bouncing back of a wave when it encounters a boundary between two media.

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Wave Function (y(x,t))

A mathematical concept that represents the shape and movement of a wave. It's a function that describes how the displacement of a point on a wave varies with time and position.

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Angular Frequency (ω)

The angular frequency of a wave, measured in radians per second. It determines how quickly the wave oscillates.

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Angular Wave Number (k)

The angular wave number of a wave, measured in radians per meter. It determines the spatial frequency of oscillations.

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Phase Constant (φ)

The initial phase of a wave, influencing its position at time zero.

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Positive Traveling Wave

A wave traveling in the positive direction of the x-axis.

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Negative Traveling Wave

A wave traveling in the negative direction of the x-axis.

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Sinusoidal Wave

Describes a wave that has a sinusoidal shape, meaning its displacement varies like a sine function.

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Fixed Phase Point

A fixed point on a wave that maintains a constant phase over time.

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Wave Speed

The speed at which a fixed phase point on a wave moves in the direction of wave propagation.

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Wave Speed Equation

The equation that describes the relationship between wave speed (v), wavelength (λ), and frequency (ν).

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Wave Speed Dependence

A wave's speed is determined by the properties of the medium through which it travels.

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Angular Frequency and Period

The mathematical relationship between angular frequency (ω) and period (T), representing the time taken for one complete cycle of oscillation.

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Wavelength and Wave Number

The mathematical relationship between wavelength (λ) and wave number (k), representing the spatial frequency of the wave.

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Speed, Angular Frequency, and Wave Number Relationship

The equation that relates wave speed (v), angular frequency (ω), and wave number (k), showing how these parameters are interconnected.

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Wave Travel in One Period

The distance travelled by a wave during one period (T) is equal to the wavelength (λ).

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Linear Mass Density (µ)

A quantity used to describe the mass per unit length of a string or wire.

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Tension (T)

The force that pulls on the ends of a string or wire, keeping it taut.

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Speed of Transverse Wave (v)

The speed at which a wave travels along a stretched string. It depends on the tension and the linear mass density of the string.

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Bulk Modulus (B)

The ability of a material to resist compression. It quantifies how much pressure is needed to change the volume of a substance.

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Speed of Longitudinal Wave (v)

The speed at which a longitudinal wave travels through a medium. It depends on the bulk modulus and the density of the medium.

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Dimensional Analysis

A process used to determine relationships between physical quantities by analyzing their dimensions. It can't determine exact formulas, but can help identify possible relationships.

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Dimensionless Constant

A constant that is often undetermined by dimensional analysis. It accounts for factors not captured by simply analyzing dimensions.

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Adiabatic Bulk Modulus

The adiabatic bulk modulus is a measure of how resistant a substance is to compression under adiabatic conditions. It's the ratio of the change in pressure to the fractional change in volume under constant entropy.

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Speed of Sound in Ideal Gases

The speed of sound in an ideal gas is proportional to the square root of the ratio of the adiabatic bulk modulus to the density of the gas.

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Adiabatic Bulk Modulus for Ideal Gas

For an ideal gas, the adiabatic bulk modulus is equal to γ times the pressure, where γ is the adiabatic index (the ratio of specific heats Cp/Cv).

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Laplace Correction

Laplace correction refers to the correction made to Newton's original formula for the speed of sound in air by incorporating the adiabatic bulk modulus instead of the isothermal bulk modulus.

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Principle of Superposition for Waves

The principle of superposition states that when two or more waves overlap, the net displacement at any point is the algebraic sum of the displacements due to each individual wave

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Wave Pulses Crossing

When two wave pulses traveling in opposite directions cross each other, the principle of superposition applies. Each pulse moves as if the other is not present, and the resultant displacement is the sum of the individual displacements.

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Net Displacement of Overlapping Pulses

The net displacement of two overlapping wave pulses can be positive, negative, or zero depending on the relative amplitudes and directions of each pulse.

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Superposition Equation

The equation y(x,t) = y1(x,t) + y2(x,t) represents the net displacement y of two wave disturbances y1 and y2 in a medium, according to the principle of superposition.

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Study Notes

Waves

  • Waves transport energy and information from one point to another without the matter itself being transported.
  • Mechanical waves require a medium, like water or air, for propagation through vibrations of the medium's particles, whereas electromagnetic waves can travel through empty space.
  • Transverse waves have oscillations perpendicular to the direction of propagation (e.g., waves on a string).
  • Longitudinal waves have oscillations parallel to the direction of propagation (e.g., sound waves).
  • The speed of a wave depends on the properties of the medium, like density and elasticity.
  • The principle of superposition states that the combined displacement of multiple waves is the algebraic sum of the individual displacements. This leads to phenomena like interference and beats.
  • Standing waves result from the superposition of two waves travelling in opposite directions, creating fixed points of zero displacement (nodes) and maximum displacement (antinodes).
  • Reflection occurs when a wave encounters a boundary; it may or may not change phase depending on the boundary's rigidity.

Types of Waves

  • Transverse: Perpendicular particle displacement to wave propagation
    • Examples include water waves and seismic S-waves.
  • Longitudinal: Parallel particle displacement to wave propagation
    • Examples include sound waves and seismic P-waves.

Wave Properties

  • Amplitude: Maximum displacement from equilibrium.
  • Wavelength: Distance between two consecutive points of the same phase.
  • Frequency: Number of oscillations per second (unit: Hertz).
  • Period: Time taken for one complete oscillation (unit: seconds).
  • Angular frequency: 2π times the frequency (unit: radians/second).
  • Angular wave number: 2π divided by wavelength (unit: radians/meter).
  • Speed: Product of frequency and wavelength.
  • Phase: Describes the position of a point on a wave cycle.

Wave Speed

  • For transverse waves on a string: speed = √(tension/linear mass density).
  • For longitudinal waves in a medium, like a gas: speed = √(bulk modulus/density).

Standing Waves

  • Created by the superposition of two or more waves travelling in opposite directions.
  • Characterized by nodes (no displacement) and antinodes (maximum displacement).

Beats

  • A phenomenon where two waves of slightly different frequencies interfere, creating a fluctuating amplitude.
  • The beat frequency is the difference between the frequencies of the two waves.

Summary of Wave Types

  • Mechanical Waves: Require a medium for propagation; examples include sound, water waves, and seismic waves.
  • Electromagnetic Waves: Do not require a medium for propagation; examples include light, radio waves, and microwaves.
    • Speed of light in a vacuum: approximately 3 x 10⁸ m/s.
  • Matter Waves: Associated with the quantum mechanical behavior of particles.

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