Here is a concise reviewer based on the Mechanical Waves module:
1. Mechanical Waves Overview
- Disturbances in matter (medium) that carry energy.
- Medium: Material through which waves propagate, e.g., air, water,
string.
- Wave Speed (v): Determined by the mechanical properties of the
medium.
2. Types of Mechanical Waves
- Transverse Waves: Particles move perpendicular to the wave
direction (e.g., waves on a string).
Note: The highest point of the wave above the rest position is the Crest.
The lowest point below the rest position is the Trough.
- Longitudinal Waves: Particles move parallel to the wave direction
(e.g., sound waves).
Note: An area where the particles in a medium are spaced close together
is called Compression (region of increased density). An area where the
particles in a medium are spread out is called Rarefaction (region of
decreased density)
- Surface Waves: Combination of transverse and longitudinal motions
(e.g., water waves). Motion of particles in circle.
3. Wave Properties
- Period (T): Time for one complete cycle.
- Frequency (f): Number of cycles per second (Hertz, Hz).
- Wavelength (λ): Distance between two corresponding points in
consecutive cycles.
- Wave Speed Formula : v = λ × f
- Amplitude (A): Maximum displacement from the rest position.
Periodic Waves: Waves where particles undergo periodic motion.
When a sinusoidal wave passes through a medium, every particle
undergoes simple harmonic motion with the same frequency.
Do not be confused! The wave moves with constant speed v along the
length of the string, while the motion of the particle is simple harmonic
and transverse (perpendicular) to the length of the string.
4. Wave Behavior
- Interference: When two or more waves meet.
- Constructive Interference: Waves combine to produce a larger
amplitude.
- Destructive Interference: Waves combine to reduce the
amplitude.
- Superposition Principle: The total displacement at any point is the
sum of individual displacements.
- Reflection: Waves bounce back when hitting a boundary.
- Fixed End: Wave is reflected and inverted.
- Free End: Wave is reflected without inversion.
5. Standing Waves
- Occurs when two waves of the same frequency and amplitude travel in
opposite directions, forming nodes (no displacement) and antinodes
(maximum displacement).
- Fundamental Frequency (f₁): Lowest frequency at which a standing
wave forms.
- Harmonics: Higher frequencies at which standing waves form.
6. Mathematical Description of Waves
- Wave Function:
- Wave Speed Relation:
- Particle Velocity (vₓ): Rate of particle motion, varies with time.
7. Energy in Waves
- Waves transport energy, not matter.
-Power of a Wave: Rate at which energy is transferred through a
medium.
- Intensity: Power per unit area, inversely proportional to the square of
the distance from the source (inverse-square law).
8. Examples and Applications
- Sound Waves: Travel faster in denser media and depend on
temperature (speed of sound in air at 20°C = 344 m/s).
- Wave on a String: Speed depends on the tension and mass per unit
length (linear density).
9. Other Notable Key Points
- the complete absence of transverse force, are called boundary
conditions.
- Nodes: Points of zero displacement.
- Antinodes: Points of maximum displacement.
- Antinodal positions - positions along the medium that vibrate back
and forth between a maximum upward displacement to a maximum
downward displacement.
The lowest possible frequency at which a string could vibrate to form a
standing wave pattern is known as the fundamental frequency or the
first harmonic.
Note: Amplitude is independent of wavelength or frequency. Increasing
the frequency decreases the wavelength, and vice versa. The amplitude of
a wave, however, does not depend on the frequency or the wavelength.
