Wave Equation and Properties of Waves

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Questions and Answers

What is the relationship expressed by the wave equation?

Wave speed equals wavelength multiplied by frequency. (correct)

Wave speed is the sum of wavelength and frequency.

Wave speed equals frequency divided by wavelength.

Wave speed equals the product of wavelength and frequency.

How can the frequency of a wave be determined using an oscilloscope?

By measuring the time taken for one complete oscillation. (correct)

By measuring the amplitude of the wave over time.

By setting the timebase on the oscilloscope to represent energy.

By analyzing the reflection coefficient of the wave.

What happens to the speed and frequency of a wave when it is refracted into a denser medium?

Both speed and frequency decrease.

Speed remains constant while frequency decreases.

Speed decreases and frequency remains constant. (correct)

Both speed and frequency increase.

What characterizes the process of diffraction?

The spreading out of a wave front as it passes through a gap. Signup and view all the answers

How does polarisation affect transverse waves?

It restricts the oscillation of the wave to a plane. Signup and view all the answers

What remains unchanged when a wave is reflected at a boundary?

The frequency and wavelength of the wave. Signup and view all the answers

When does maximum diffraction occur?

When the gap size is close to the wavelength. Signup and view all the answers

What is the effect of wavelength on the behavior of waves when entering a new medium?

Wavelength remains unchanged while speed decreases. Signup and view all the answers

Why cannot longitudinal waves experience polarization?

Their oscillation direction is limited to one plane. Signup and view all the answers

What occurs to light intensity when one polarizing filter is rotated 90° relative to another?

It decreases to a minimum. Signup and view all the answers

What does the intensity of a progressive wave depend on?

The radiant power and surface area. Signup and view all the answers

How does the intensity of light relate to the distance from a point source?

It is inversely proportional to the square of the distance. Signup and view all the answers

What is the orientation of the electric field for plane polarized microwaves transmitted through a metal grille?

Vertical. Signup and view all the answers

What type of wave are electromagnetic waves classified as?

Transverse progressive waves. Signup and view all the answers

How is the amplitude of a wave related to its intensity?

Intensity is proportional to the square of the amplitude. Signup and view all the answers

What happens to microwaves when the metal grille is rotated to a horizontal orientation?

The signal received falls to a minimum. Signup and view all the answers

What happens to a ray of light when it enters a new medium at an angle?

It experiences reflection and refraction. Signup and view all the answers

What is the condition necessary for total internal reflection to occur?

Light must travel from a higher refractive index to a lower refractive index. Signup and view all the answers

How can the angle of refraction be calculated when light passes from one medium to another?

Using the formula $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$ Signup and view all the answers

What defines constructive interference of waves?

The individual displacements are in the same direction. Signup and view all the answers

What happens during destructive interference of waves?

The individual displacements cancel each other out. Signup and view all the answers

What determines the refractive index of a medium?

The speed of light in vacuum. Signup and view all the answers

The critical angle is defined as the angle of incidence...

above which total internal reflection occurs. Signup and view all the answers

What does the principle of superposition state?

The resultant displacement at a point is the sum of individual displacements. Signup and view all the answers

What is the primary characteristic of nodes in a stationary wave?

They always have zero amplitude. Signup and view all the answers

How far apart are two adjacent nodes in a stationary wave?

Half a wavelength apart. Signup and view all the answers

What happens to energy in stationary waves?

They store energy without transferring it. Signup and view all the answers

What role does the vibration generator play in producing a stationary wave in a stretched string?

It oscillates the string in a coherent manner. Signup and view all the answers

What occurs at the ends of a string when producing a stationary wave?

Nodes are formed at both ends. Signup and view all the answers

In an air-filled tube that is closed at one end, what type of wave is formed?

An antinode is at the open end and a node at the closed end. Signup and view all the answers

The phase difference between two points on a stationary wave is given by what expression?

180°n Signup and view all the answers

What is the fundamental frequency of a stationary wave?

The lowest frequency of vibration for a given arrangement. Signup and view all the answers

What condition must be met for two waves to be considered coherent?

They must have a constant and unchanging phase difference. Signup and view all the answers

When does maximum resultant displacement occur during wave interference?

When the phase difference is an even multiple of π. Signup and view all the answers

Which method is typically used to investigate superposition in light waves?

Double-slit experiment. Signup and view all the answers

In the Young double-slit experiment, what does the variable 'd' represent?

The distance between the slits and the screen. Signup and view all the answers

What does the equation $\lambda = \frac{a}{d}$ help determine in the context of wave interference?

The wavelength of the light used. Signup and view all the answers

What is the term used for the angle between the 0th and nth maxima in wave interference?

Theta (θ). Signup and view all the answers

How does a diffraction grating create an interference pattern?

By allowing light to pass through transparent slits. Signup and view all the answers

What is referred to as 'n' in the context of maxima in interference patterns?

The order of maxima. Signup and view all the answers

What does Kirchhoff’s first law state about currents at a point in an electrical circuit?

The sum of the currents entering a point is equal to the sum of the currents leaving that point. Signup and view all the answers

What is the primary direction of conventional current?

From positive to negative terminal. Signup and view all the answers

In which type of material would you expect the mean drift velocity of electrons to be the highest?

Conductors such as metals. Signup and view all the answers

What happens to the speed of electrons in a material with a lower number density while maintaining the same current?

Electrons must travel faster to carry the same current. Signup and view all the answers

What do cations and anions do when electrodes are placed in a solution?

Cations are attracted to the anode and anions are attracted to the cathode. Signup and view all the answers

What is the SI unit of electric current?

Ampere Signup and view all the answers

How is the net charge of a particle calculated?

Q = ± ne Signup and view all the answers

Which of the following describes how current flows in metals?

Electrons are the charge carriers Signup and view all the answers

What happens to a neutral atom when it gains electrons?

It becomes a negative ion Signup and view all the answers

What is the role of an ammeter in an electrical circuit?

It measures current Signup and view all the answers

In ionic solutions, what particles are primarily responsible for conducting electricity?

Positive and negative ions Signup and view all the answers

What happens to the charge of a particle when electrons are removed?

It becomes a positive ion Signup and view all the answers

What does the flow of charge equal in terms of current?

Charge divided by time Signup and view all the answers

Study Notes

Wave Equation and Frequency

The wave equation relates wave speed (v), wavelength (λ), and frequency (f): v = fλ.
The equation can be rewritten as v = 1/T, where T is the period of the wave, the time for one complete oscillation.

Determining Wave Frequency

An oscilloscope can be used to measure the frequency of a wave.
The timebase of the oscilloscope represents time on the x-axis and amplitude on the y-axis.
By measuring the time for one complete oscillation, the frequency can be calculated.

Reflection, Refraction, Diffraction, and Polarization

Waves can be reflected, refracted, and diffracted.
Reflection: A wave changes direction at a boundary between two media, remaining in the original medium.
Refraction: A wave changes direction as it changes speed when entering a new medium.
Diffraction: A wave spreads out as it passes through a gap.
Polarization: A property of transverse waves where the oscillation is restricted to one plane.

Demonstrating Wave Effects

Ripple tank: Demonstrates reflection, refraction, and diffraction of water waves.
Polarizing filters: Demonstrate polarization of light.
Metal grille: Demonstrates polarization of microwaves.

Intensity of a Progressive Wave

Intensity is the power passing through a surface per unit area (P/A).
Units are watts per square meter (Wm⁻²).
Intensity is inversely proportional to the square of the radius for a point source.
Intensity is proportional to the square of the amplitude of the wave.

Electromagnetic Waves

Electromagnetic waves are transverse progressive waves with oscillating electric and magnetic fields.
They travel through a vacuum at a speed of 3.0 x 10⁸ m/s.
Visible light is a small part of the electromagnetic spectrum.

Refraction of Light

When light travels from one medium to another, it refracts due to a change in speed.
Refractive index (n) is the ratio of the speed of light in a vacuum to the speed of light in the medium.
Snell's Law relates the angles of incidence and refraction: n₁sinθ₁ = n₂sinθ₂.

Total Internal Reflection

Occurs when light travels from a medium with a higher refractive index to a medium with a lower refractive index.
The critical angle (C) is the angle of incidence above which total internal reflection occurs.
The formula for the critical angle is sinC = 1/n, where n is the refractive index of the material the light is entering.

Superposition

The principle of superposition states that when waves meet, the resultant displacement is the sum of the individual wave displacements.
Constructive interference: Displacements in the same direction add together.
Destructive interference: Displacements in opposite directions cancel each other out.

Interference and Coherence

Two waves are coherent if they emit with a constant and unchanging phase difference.
Interference occurs when coherent waves superpose.
The maximum resultant displacement occurs when the phase difference is an even multiple of π.
The minimum resultant displacement occurs when the phase difference is an odd multiple of π.

Investigating Superposition and Wavelength

Audio signal generators: Investigate superposition in sound waves by creating an interference pattern.
Young's double-slit experiment: Investigate superposition and determine the wavelength of light.
Diffraction grating: Investigate the wavelength of light.

Stationary Waves

Formed when two progressive waves with the same frequency traveling in opposite directions superpose.
Characterized by nodes (zero amplitude) and antinodes (maximum displacement).
Frequency is the same at all points except at the nodes.

Producing Stationary Waves

Stretched string: A vibrating generator creates waves that reflect, forming a stationary wave.
Microwaves: A transmitter and a reflecting surface create a stationary wave.
Sound in a tube: A tuning fork creates sound waves that interfere, forming a stationary wave depending on the tube's length and end conditions.
The fundamental frequency is the lowest frequency of vibration for a given arrangement.

Charge

Charge is a physical quantity that can be positive or negative.
Charge is measured in Coulombs (C) where 1 Coulomb is the amount of charge that flows in 1 second when the current is 1 Ampere.
Like charges repel, while opposite charges attract.
The charge of ions and atomic components is quantised.
A proton has a charge of +1 and an electron has a charge of -1.
These charges are multiples of the elementary charge (e) which is 1.6 x 10⁻¹⁹ C.
The net charge of a particle is due to the gain or loss of electrons.
A neutral atom has an equal number of protons and electrons.
Increasing the number of electrons creates a negative ion.
Removing electrons creates a positive ion.
The net charge on a particle (Q) is given by Q = ± ne, where n is the number of electrons added or removed and e is the elementary charge.

Electric Current

Electric current (I) is the rate of flow of charge.
Current is measured in Amperes (A).
Current is calculated as I = dQ/dt.
An ammeter is used to measure current and is placed in series in a circuit.

Charge Carriers

Electric current is the rate of flow of charge, but charge can be carried in different ways depending on the material.
In metals, current is carried by electrons.
Metals have a lattice of positive ions surrounded by free electrons.
The positive ions are fixed, but the electrons can move.
When a potential difference is applied across a metal, electrons are attracted to the positive terminal and create a current.
Some liquids can conduct charge, these are called electrolytes and are typically ionic solutions.
Electrolytes contain positive and negative ions.
When electrodes are placed in an electrolyte, cations are attracted to the cathode and anions are attracted to the anode, leading to an electric current.

Conventional Current

Conventional current is the flow of charge from the positive to the negative terminal.
This is the standard way current is treated, regardless of the actual direction of charge carriers.
In metals, electrons flow from negative to positive, so the electron flow is opposite to the conventional current.

Kirchhoff’s 1st Law

Kirchhoff's 1st law states that at any point in an electrical circuit, the sum of the currents into that point is equal to the sum of the currents out of that point.
This is a consequence of the conservation of charge.
Charge cannot be created or destroyed, only transferred.

Mean Drift Velocity

Electrons in a metal move randomly due to collisions with positive ions.
When a potential difference is applied, the electrons are attracted to the positive terminal, but still collide with positive ions.
Mean drift velocity (v) is the average velocity of electrons as they travel through the wire.
The number density (n) of a material is the number of free electrons per unit volume.
Conductors have high number densities (around 10²⁸ per m³).
Insulators have much lower number densities and semi-conductors have values in-between.
Lower number densities mean electrons must travel faster to carry the same current.
Current can be calculated as I = nAve, where A is the cross-sectional area of the wire and e is the elementary charge.

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Description

Explore the fundamentals of wave behavior through this quiz on the wave equation, frequency, reflection, refraction, diffraction, and polarization. Test your understanding of how these concepts interact and their practical applications using tools like oscilloscopes.