General Physics Chapter 16: Wave Motion

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Questions and Answers

What is a wave defined as?

  • A propagation of a disturbance into space (correct)
  • A force acting on objects in motion
  • A movement of particles in isolation
  • A static disturbance in space

Mechanical waves do not require a medium to propagate.

False (B)

What is the main characteristic of wave motion?

Energy is transferred over a distance, but matter is not.

A wave that causes particles in the medium to move ____ to the direction of propagation is called a longitudinal wave.

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

Which of the following is an example of a transverse wave?

<p>Visible light (D)</p> Signup and view all the answers

Match the types of waves with their characteristics:

<p>Longitudinal waves = Particles move parallel to wave direction Transverse waves = Particles move perpendicular to wave direction Mechanical waves = Require a medium to propagate Electromagnetic waves = Do not require a medium</p> Signup and view all the answers

Name one type of wave that is considered electromagnetic.

<p>X-rays</p> Signup and view all the answers

Water waves are classified as electromagnetic waves.

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

What does the wavelength (λ) represent in wave motion?

<p>The minimum distance between identical points on adjacent waves (D)</p> Signup and view all the answers

A high energy wave is characterized by a high amplitude.

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

What is the unit of frequency?

<p>hertz (Hz)</p> Signup and view all the answers

The time it takes for vibrating particles in a wave to complete one cycle is called the ______.

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

Which relationship exists between wavelength (λ) and frequency (f)?

<p>As wavelength decreases, frequency increases. (B)</p> Signup and view all the answers

Match the parameters related to waves with their definitions:

<p>Wavelength (λ) = Minimum distance between identical points on adjacent waves Frequency (f) = Number of cycles that occur in one second Amplitude = Maximum value of the wave Wave velocity (v) = Displacement traveled by the wave in one second</p> Signup and view all the answers

The amplitude of a wave does not affect the energy it transports.

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

How is wave velocity (v) related to frequency and wavelength?

<p>Wave velocity is the product of frequency and wavelength (v = f * λ).</p> Signup and view all the answers

What is the y coordinate in the wave function y(x, t) equivalent to?

<p>The transverse position of an element (B)</p> Signup and view all the answers

A pulse traveling to the right on a string can be represented as y(x, t).

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

What term describes the maximum displacement of a particle in a wave from its equilibrium point?

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

A wave that travels in the direction of the oscillation is called a ______ wave.

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

If a wave function describes a pulse traveling to the left, which form of the wave function is used?

<p>y(x, t) = f(x + vt) (A)</p> Signup and view all the answers

The wave function y(x, t) can only represent longitudinal waves.

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

What is the significance of the variable 't' in the wave function y(x, t)?

<p>It represents time.</p> Signup and view all the answers

Match the wave characteristics with their definitions:

<p>Amplitude = Maximum displacement from equilibrium Wave Speed = Distance traveled per unit time Wavelength = Distance between successive crests Frequency = Number of waves per unit time</p> Signup and view all the answers

What is the relationship between the power of a sinusoidal wave and its amplitude?

<p>Power is proportional to the square of the amplitude. (C)</p> Signup and view all the answers

The intensity of a wave is inversely proportional to its amplitude.

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

What is the angular frequency of the wave if the frequency is 8.00 Hz?

<p>50.27 rad/s</p> Signup and view all the answers

The wave number k for a wave with a wavelength of 40.0 cm is _____.

<p>0.157 rad/cm</p> Signup and view all the answers

Match the following terms related to sinusoidal waves with their definitions:

<p>Wavelength = Distance between two consecutive points in phase Amplitude = Maximum displacement from the rest position Frequency = Number of cycles per second Phase constant = Initial angle of the wave at t=0 and x=0</p> Signup and view all the answers

Which quantity is NOT a property of a sinusoidal wave?

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

The wave function can change when the phase constant is altered.

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

If the wave moves to the right with a speed v, how can it be mathematically expressed?

<p>y(x, t) = A sin(kx - ωt + Φ)</p> Signup and view all the answers

What is the frequency of a sound wave with a wavelength of 3.00 m, given that the speed of sound is 343 m/s?

<p>114.33 Hz (D)</p> Signup and view all the answers

What is the frequency of a light wave with a wavelength of 3.00 m, given that the speed of light is 3 × 10^8 m/s?

<p>1 × 10^9 Hz (A)</p> Signup and view all the answers

The speed of a wave can be determined by the product of frequency and wavelength.

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

What is the wavenumber of a wave if k = 2.7 rad/m?

<p>2.7 rad/m</p> Signup and view all the answers

The formula to calculate frequency is ___ = speed / wavelength.

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

What is the vertical position of an element of the string at t = 0, x = 0.100 m for the given wave function?

<p>Requires further calculation based on the wave function.</p> Signup and view all the answers

Match the following wave parameters with their respective definitions:

<p>Frequency = Number of cycles per second Wavelength = Distance between consecutive crests Speed = Rate at which the wave propagates Wavenumber = Number of radians per unit distance</p> Signup and view all the answers

When comparing the given wave equation, we note that sin(θ) = _____.

<p>−sin(−θ)</p> Signup and view all the answers

What is the wavelength of a wave if it travels 425 cm in 10.0 s, given its frequency is 1.33 Hz?

<p>63.75 cm (C)</p> Signup and view all the answers

The amplitude of a sinusoidal wave can be defined as the maximum distance from the equilibrium position.

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

Calculate the angular frequency of a wave with a frequency of 5 Hz.

<p>31.42 rad/s</p> Signup and view all the answers

The _______ of a wave is defined as the time it takes for one complete cycle.

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

If two waves have the same wave speed, but one has frequency f and the other has frequency 2f, what can be said about their wavelengths?

<p>Wavelength of second wave is half the first (C)</p> Signup and view all the answers

A wave with a higher frequency always has a greater amplitude than a wave with a lower frequency.

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

Describe the phase shift of a wave if its equation is given as y = 2sin(3x - π/4).

<p>π/4 to the right</p> Signup and view all the answers

Match the terms related to wave properties with their definitions:

<p>Wavelength = Distance between consecutive crests Frequency = Number of cycles per unit time Amplitude = Maximum displacement from equilibrium Wave speed = Distance traveled by a wave in a unit time</p> Signup and view all the answers

Flashcards

Mechanical wave

A wave that needs a medium to travel.

Electromagnetic wave

A wave that does not need a medium to travel.

Longitudinal wave

A wave where the medium moves parallel to the wave's direction.

Transverse wave

A wave where the medium moves perpendicular to the wave's direction.

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Wave propagation

The movement of a disturbance through space.

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Wave

A disturbance that travels through space.

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Medium

A substance or material through which a mechanical wave travels.

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Energy Transfer

Energy moves while the matter stays in place.

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Wave Function

A mathematical equation that describes the position of a point on a wave (y-coordinate) as a function of position (x) and time (t).

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Amplitude (A)

The maximum displacement from the equilibrium position of a vibrating particle in a wave.

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Wave Function y(x,t)

Mathematical representation providing the transverse position (y) of any point (x) on a wave at a specific time (t).

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Sinusoidal Wave

A wave whose shape is described by a sine or cosine function.

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Equilibrium Position

The resting position of a vibrating particle before a wave passes.

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Wavelength (λ)

Shortest distance between two identical points on adjacent waves, like crest-to-crest or trough-to-trough.

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Period (T)

Time for a particle in a wave to complete one cycle.

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Frequency (f)

Number of waves passing a point per unit time (usually 1 second).

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Wave Velocity (v)

Distance a wave travels in one second, related to frequency and wavelength.

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High Frequency

Shorter Wavelength

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Wave Energy

Related to the amplitude (height) of a wave.

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Transverse wave function

Mathematical description of a transverse wave, including amplitude and phase constant.

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Amplitude

Maximum value of a wave's displacement from equilibrium.

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Wave Frequency

The number of wave cycles passing a fixed point per unit of time. Measured in Hertz (Hz).

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Wavelength

The distance between two consecutive crests or troughs of a wave. Measured in meters (m).

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Wave Speed

The distance a wave travels per unit of time. Calculated by multiplying frequency by wavelength.

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Angular Frequency (ω)

The rate at which a wave oscillates or cycles in radians per second. Related to frequency by ω = 2πf.

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Wavenumber (k)

The spatial frequency of a wave, indicating how many cycles occur per unit of distance. Measured in radians per meter (rad/m).

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Wave Equation

A mathematical expression describing the displacement of a wave at any point in space and time. It typically involves sinusoidal functions like sine or cosine.

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How to find wave speed from the wave equation?

The speed of a wave can be determined from its angular frequency (ω) and wavenumber (k) using the equation: v = ω/k.

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What is the direction of a wave given its equation?

The sign of the term involving x inside the trigonometric function (sine or cosine) tells wave travel direction. A positive sign indicates a wave traveling in the negative x-direction, and vice-versa.

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Frequency

The number of complete oscillations or cycles a wave makes in one second. It is measured in Hertz (Hz).

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Wave number

A measure of the spatial frequency of a wave. It is the number of wavelengths per unit distance, measured in radians per meter (rad/m).

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Angular frequency

A measure of how quickly the wave oscillates. It is the angular displacement of the wave per unit time, measured in radians per second (rad/s).

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Phase shift

A change in the position of a wave relative to a reference point. It is a measure of how much a wave is shifted horizontally or vertically.

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Period

The time it takes for one complete oscillation or cycle of a wave to occur. It is measured in seconds (s).

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Wave Speed Formula

The speed of a sinusoidal wave is calculated by multiplying the wavelength by the frequency: v = fλ.

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Power of a Wave

The power of a sinusoidal wave, representing the energy transferred per unit time, is proportional to the square of the frequency and the square of the amplitude.

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Wave Intensity

The intensity of a wave measures the energy flow per unit area. It's directly proportional to the square of the wave's amplitude.

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Phase Constant (Φ)

The phase constant determines the wave's initial position at time t = 0. It's a value that shifts the wave horizontally along the x-axis.

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Study Notes

General Physics (42104) - Chapter 16: Wave Motion

  • Wave: A propagation of a disturbance into space.
  • Mechanical Waves: Require a medium to be disturbed
    • Longitudinal Waves: Elements of the medium move parallel to the direction of propagation. Examples: Sound waves
    • Transverse Waves: Elements of the medium move perpendicular to the direction of propagation. Examples: Water waves, visible light, x-rays, infrared rays.
  • Electromagnetic Waves: Do not require a medium. Examples: Visible light, x-rays, infrared rays.
  • Wave Function: y(x,t) = represents the y-coordinate (transverse position) of an element at position x at time t.
    • y(x,t) = f(x – vt) if pulse travels right
    • y(x,t) = f(x + vt) if pulse travels left
  • Wave Characteristics:
    • Amplitude (A): Maximum displacement of a vibrating particle from its equilibrium point.
    • Wavelength (λ): Minimum distance between two identical points on adjacent waves (e.g., crest to crest, trough to trough). Usually measured in cm.
    • Period (T): Time for one cycle of vibration. Measured in seconds per cycle.
    • Frequency (f): Number of complete cycles per unit time (usually 1 second). Measured in Hertz (Hz) or s⁻¹.
    • Wave Velocity (v): Displacement traveled by the wave in one second. Relates to frequency and wavelength: v = λf
  • Energy and Amplitude:
    • The amount of energy carried by a wave is related to the amplitude. High energy waves = High amplitude; Low energy waves = low amplitude
  • Wave Function for a Transverse Wave: y(x, t) = A sin(kx + wt + φ). Where:
    • A = amplitude
    • k = angular wave number
    • ω = angular frequency
    • φ = phase constant
    • v = wave speed; v = ω/k = λf
    • Direction is determined by the sign ( + or - ) in the wave function
  • Power of a Wave: Proportional to the square of the angular frequency and the square of the amplitude.
  • Wave Intensity: Proportional to the square of the amplitude; Intensity = Power/Area

Examples (Calculations and Applications)

  • Example 1: Finding wave number, period, angular frequency, and speed of a sinusoidal wave given amplitude, wavelength, and frequency. Includes calculations.
  • Example 2: Calculating the frequency of a wave given its wavelength and speed (for sound and light waves).
  • Example 3: Determining frequency, wavelength, and speed of a wave from its displacement equation.
  • Example 4: Calculating the speed and direction of a traveling wave given its wave function.
  • Example 5: Determining the frequency and wavelength of a wave given the number of vibrations completed in a time and distance traveled.
  • Additional Example: Solving for various parameters (amplitude, wave number, angular frequency, wave speed, wavelength, and period) of a wave given the wave function

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General Physics (42104) Chapter 16: Wave Motion PDF

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