Notes, summaries, assignments, exams, and problems for Physics

1. Definitions

Sound: A wavelength above the atmospheric pressure, with a frequency range between 20 Hz and 20 kHz. The pressure range is between 2.10^-5 and 200 Pa for 1 kHz (for the rest of the region bounded by the isophone hearing threshold and the threshold of pain).
Wave: A disturbance that propagates, transporting energy but not matter.
Pressure: Force / Surface
Fletcher and Munson Curves (Isophone Curves): These curves represent the sensitivity of the ear to different frequencies, in addition to indicating the minimum pressure in dB required to start hearing.
Audible Range: The area bounded by the isophone hearing threshold and pain threshold curves, and the frequencies 20 Hz and 20 kHz.

2. Representation: Time and Frequency Domain

Pure Sound:

Wave Phenomena: Reflection and Refraction

The study of wave phenomena, such as reflection and refraction, is fundamental to understanding how waves interact with different environments.

When a wave encounters a boundary between two media, part of its energy is reflected, continuing to spread within the original environment. The other part of the wave passes through the boundary, undergoing refraction.

To analyze these phenomena, we establish the concept of a normal: an imaginary line perpendicular to the surface at the point of incidence. Key angles involved are:

• (I) Incidence Angle: The angle between the incident ray and the normal.
• (r) Reflection Angle: The angle between the reflected ray and the normal.
• (R) Refraction Angle: The angle between

Simple Harmonic Motion: Energy Analysis

The energy of a particle performing simple harmonic motion is composed of two contributions: the kinetic energy E_c, associated with the particle's velocity, and the potential energy E_p, due to the restoring force. The displacement of the movement is described by the expression x = A sin (ωt + φ), speed is v = dx / dt = Aω cos (ωt + φ), and the acting force (F = -Kx) is associated with a potential energy of elastic type: E_p = ½ kx².

Potential and Kinetic Energy Equations

Thus, the potential energy is E_p = ½ kA²sin²(ωt + φ), and the kinetic energy is: E_c = ½ mv² = ½ mA²ω²cos²(ωt + φ) = ½ kA²cos²(ωt + φ) where k = mω²

Total Energy in Simple Harmonic Motion

Therefore, the total energy is: E_t... Continue reading "Simple Harmonic Motion: Kinetic and Potential Energy Analysis" »

The Theory of Relativity: Revolution in the Macrocosm

Einstein published the theory of special relativity in 1905. Space and time are, therefore, a four-dimensional continuum. Einstein generalized this theory with the theory of general relativity. One of the underlying principles of relativity is that nothing can go faster than light, even gravitational interaction. It was, therefore, necessary to develop the theory of gravitation, taking this limit into account. To achieve this, Einstein introduced the idea of a gravitational field. In the proximity of a large body, space is curved, and time passes more slowly. If space is curved, the planets draw an orbit around it. Thus, the theory of relativity explains the orbital motions of the planets.... Continue reading "Relativity, Universe Expansion, and Wave-Particle Duality" »

Classification of Optical Methods

Non-Spectroscopic Techniques

• Refractometry
• Polarimetry

Spectroscopic Techniques

• UV-Vis Spectrophotometry
• Atomic Absorption
• Flame Photometry

Classification of Spectroscopic Methods

Spectroscopic methods are categorized by absorption or emission.

Absorptiometry

This electromagnetic method uses light, which has both corpuscular and wave-like characteristics. Light is broken down into different wavelengths, arranged in what is called the electromagnetic spectrum.

Wave Constitution

A wave consists of two fields—electric and magnetic—perpendicularly intersecting each other and propagating in the direction of the wave.

Speed of Wave Propagation

In a vacuum, the speed of light (c) is 3x10¹⁰ cm/sec. This speed can change when... Continue reading "Spectroscopic Techniques in Optical Methods: A Comprehensive Guide" »

Study of Reflection and Refraction of Electromagnetic Waves

Objectives

• Measure the refractive index of a prism for electromagnetic waves in the visible range (light) and for microwaves.
• Measure the angle of reflection of electromagnetic waves.
• Determine the critical angle when a ray of light passes from a medium of higher refractive index to one of lower refractive index, leading to total internal reflection.

Theoretical Background and Planning

Refraction occurs when a wave changes its propagation speed upon passing from one medium to another. This phenomenon changes the direction of the ray when it is incident obliquely to the interface between two media with different refractive indices.

This relationship is governed by Snell's Law:

n₁ sin θ_i =... Continue reading "Experimental Determination of Refractive Index Using Light and Microwaves" »

Understanding Uniform Circular Motion

In uniform circular motion, an object's body movement describes circular arcs of equal length (n equal times). The magnitude of the linear velocity (dl) is constant, but its direction changes continuously.

Linear Speed

Linear speed (s) is the angular velocity multiplied by the radius vector (xl).

Centripetal Acceleration

Centripetal acceleration is perpendicular to the path (dl) and is always directed toward the center of the circle.

Period and Frequency

In uniform circular motion:

• Period (T): The time it takes for an object to complete one full revolution.
• Frequency (f): The number of revolutions an object completes per unit of time.

Centripetal Force

Centripetal force is the force responsible for maintaining circular... Continue reading "Understanding Uniform Circular Motion: Concepts & Theories" »

Kinetic Energy and Potential Energy

Kinetic Energy (KE) Calculation:

A body with a mass of 50kg has a velocity of 20 m/s.

KE = (1/2) * M * V²

KE = (1/2) * 50kg * (20 m/s)²

KE = (1/2) * 50 * 400

KE = 10000 Joules

Total Energy Calculation:

A body with a mass of 5kg is at a height of 10m and moving at a speed of 20 m/s. Calculate its total energy.

Mass (M) = 5kg

Height (H) = 10m

Velocity (V) = 20 m/s

Potential Energy (PE) = M * g * H = 5kg * 9.8 m/s² * 10m = 490 Joules

Kinetic Energy (KE) = (1/2) * M * V² = (1/2) * 5kg * (20 m/s)² = 1000 Joules

Total Energy = KE + PE = 1000 Joules + 490 Joules = 1490 Joules

Heat Transfer and Temperature Conversion

Kelvin to Celsius Conversion:

How to convert 300 Kelvin to Celsius, as applicable to converting 100 Celsius to Kelvin.... Continue reading "Kinetic Energy, Heat Transfer, and Algebraic Equations" »

Kinematics Formulas

Position Vector

r = xi + yj

• x = r cos
• y = r sin
• r = √(x² + y²)
• tan θ = y / x

Displacement

Δr = r - r_initial

Speed, Average Speed, Instantaneous Speed

• Average Speed: v_av = Δr / Δt
• Instantaneous Speed: v = dr / dt

Average Acceleration, Instantaneous Acceleration

• Average Acceleration: a_av = Δv / Δt
• Instantaneous Acceleration: a = dv / dt

Uniform Rectilinear Motion (MRU)

• v = Δx / Δt
• v_mean = (v₀ + v) / 2
• v = v₀ + at
• x = x₀ + vt
• x = x₀ + v₀t + (1/2)at²
• v² - v₀² = 2aΔx
• v² = v₀² ± 2as

Free Fall

• Velocity: v = gt
• Position (height fallen): y = (1/2)gt²
• Velocity (upward): v = -gt
• Position (height): y = y₀ - (1/2)gt²

Upward Vertical Launch

• Velocity: v = v₀ - gt
• Position (height): y = y₀ + v₀t - (1/2)gt²
• Time to reach maximum height: t = v₀ / g
• Maximum

Magnetic Hysteresis in Ferromagnetic Materials

When a magnetic material is subjected to a changing magnetic field intensity (H), the magnetic induction (B) lags behind. This phenomenon is known as magnetic hysteresis. (See Figure 1). When a ferromagnetic substance is subjected to a cyclical (alternating positive and negative) magnetic field intensity, it traces a hysteresis loop.

Key points on the hysteresis curve (See Figure 1):

• O-B: Magnetization curve.
• O-R: Residual magnetization.
• O-D: Coercive force.

When applying an alternating magnetization intensity (+ and -) to a ferromagnetic substance, the resulting hysteresis loop is shown in the image. The magnetic induction (B) lags behind the magnetic field intensity (H). At point B, even when H = 0,... Continue reading "Magnetic Hysteresis & Autoinduction Explained" »