Acoustics and Oscillations

Oscillations and Acoustics

• Definition of Oscillation:

  • A periodic change at regular speed of a physical quantity.
  • The quantity shifts from equilibrium and returns to its original position.
  • Types: Mechanical, Electromagnetic, Thermal, etc.

• Importance of Periodism:

  • Vital in organisms; many biological processes rely on periodicity.

Periodic Processes in Organisms

• Examples of Periodic Processes:
  • Insulin secretion every 5-6 minutes.
  • Heart pumping.
  • Breathing cycles.
  • Melatonin secretion in the brain.
  • Temperature patterns (e.g., max temp at 5:00 AM).

Mechanical Oscillating Systems

• Components:
  • Massless rod, bob (weight), gravitational force from Earth.
  • External forces can influence if the system is not isolated.

Mathematical Pendulum Dynamics

• Forces Involved:

  • Gravitational force (mg) and tension force (T) act on the bob.
  • Upon displacement, mg is not balanced by T leading to oscillation toward equilibrium.

• Definitions:

  • Period (T): Time for one complete oscillation.
  • Frequency (f): Number of cycles per unit time (units of Hertz, Hz).

Types of Oscillations

• Free vs. Forced Oscillations:
  • Free Oscillation: Internal forces only (damped amplitudes over time).
  • Forced Oscillation: Internal and external forces (can be non-damped).

Simple Harmonic Motion (SHM)

• Definition:

  • Periodic motion with a restoring force proportional to displacement.
  • Follows sine or cosine laws.

• Energy in Simple Harmonic Motion:

  • Total energy = Kinetic Energy (KE) + Potential Energy (PE).
  • Max PE when displacement is at its highest; max KE at equilibrium.

The Law of Conservation of Mechanical Energy

• Conservation Rule:
  • Mechanical energy is conserved in the absence of dissipative forces (friction, etc.).

Damping and Resonance

• Damping Ratio:

  • Ratio of successive amplitudes of oscillation.

• Resonance:

  • Tendency of a system to oscillate at greater amplitude at specific frequencies.
  • Can be beneficial (e.g., MRI) or harmful (e.g., structural damage in organs).

Auto-Oscillations

• Definition:
  • Type of forced oscillation where a system generates its own energy and maintains oscillations (e.g., mechanical clocks, heart pumping).

Mechanical Waves

• Definition:

  • Propagation of oscillations through an elastic medium (distinguished from electromagnetic waves).

• Types of Mechanical Waves:

  • Longitudinal: Oscillation occurs along the direction of wave propagation.
  • Transverse: Oscillation occurs perpendicular to wave propagation.

Wave Basics

• Wavelength (λ): Measure between two successive peaks (crests) or troughs.
• Amplitude: Measure of wave displacement from its rest position.

Wave Properties

1. Interference: Interaction of waves causing amplification (constructive) or cancellation (destructive).
2. Diffraction: Waves bending around obstacles.
3. Reflection: Waves bouncing off a boundary; angles of incidence equal angles of reflection.
4. Refraction: Change in wave direction upon passing into different media (Snell's Law).
   [ n1 imes ext{sin}(c) = n2 imes ext{sin}(eta) ]
   (where ( n1, n2 ) are the indices of refraction.)

Sound Waves

• Types & Characteristics:

  • Types of Sound:
  • Musical tones: single frequency (pure tone).
  • Complex tones: mixture of frequencies.
  • Noise: complex wave patterns without a repeating nature.

• Physical Parameters:

  • Wavelength, frequency, amplitude, speed, intensity, impedance.
  • Intensity defined in Watts; 1 Watt is Joule per second.

• Acoustic Impedance:

  • Resistance to sound transmission in a material.
  • Formula: ( Z = pV ) (where ( p ) is density, ( V ) is velocity).

Sound Spectrum

• Divided into:
  • Infrasound (<20 Hz): Natural phenomena (storms, earthquakes).
  • Acoustic Sound (20-20,000 Hz): Frequencies humans can hear.
  • Ultrasound (>20,000 Hz): Applications in medicine (e.g., imaging).

Auditory System Function

• Process:
  • Sound created in trachea during exhalation, modulated by the mouth.
  • Amplified through ear canal and transferred to inner ear via vibrations.

Sound Measurements

• Intensity Measurement:
  • Measured in Bels (logarithmic scale); reference intensity of 10^-12 W/m².
  • Loudness perceived in Phons, comparing intensity levels over the frequency spectrum.

Ultrasound in Medicine

• Characteristics:
  • Utilized for diagnostics (e.g., organ imaging) and therapies (e.g., tissue healing).

Doppler Effect

• Definition:
  • Change in wave frequency due to movement of source or observer.
  • Used in medical imaging to measure blood flow.

Summary

• Understanding acoustics and oscillations is crucial across physics, biology, and medical applications. The principles govern how waves propagate and interact with systems, informing both theoretical and practical applications in various fields.