Waves: Grade 11 Important Points
I. Introduction to Waves
• Waves are patterns that transfer energy without the actual physical matter as a
whole being transported.
• Waves transport energy and the pattern of disturbance from one location to
another.
• Not all waves require a medium for their propagation.
II. Types of Waves
A. Mechanical Waves
• Require a medium for propagation; cannot propagate through a vacuum.
• Involve oscillations of constituent particles and depend upon the properties of
the medium.
• Examples: Sound waves, water waves, seismic waves.
B. Electromagnetic (EM) Waves
• Do not necessarily require a medium; can travel in a vacuum.
• Examples: Light, radio waves, X-rays, etc..
• In a vacuum, all EM waves have the same speed (c).
C. Matter Waves
• Associated with constituents of matter (e.g., electrons, protons, molecules).
• Arise in quantum mechanical description.
• More complex than mechanical or EM waves.
• Used in a microscope.
III. Propagation of Sound Waves
A. Sound Waves in Air
• As the wave passes through air, it compresses or expands a small volume of air.
, • This causes a change in the density (\Delta\rho) and a corresponding change in
the pressure (\Delta p).
• The change in pressure induces a restoring force.
• The quantity similar to extension or compression of a spring is \Delta s.
• If a region is compressed, molecules are packed together, increasing density.
They tend to move out to the adjoining region, thereby rarefying the original
region.
• The rarefaction moves from one region to another, making compression and
rarefaction possible in air.
B. Sound Waves in Solids (Crystalline)
• Atoms are arranged in a lattice structure.
• Each atom is in equilibrium due to a force from surrounding atoms.
• Displacing one atom leads to restoring forces.
• Propagation of sound waves in fluids as well as solids can sustain compressive
strain.
• Transverse waves can only be propagated in media which can sustain shearing
stress, such as solids, but not in fluids.
C. Waves on Water Surface
• Capillary waves (Ripples): Short wavelength. Restoring force is produced due to
surface tension.
• Gravity Waves: Wavelength ranging from a few centimetres to several 100 m.
Restoring force is the pull of gravity which tends to keep the water surface at its
lowest level.
• Waves in the ocean are a combination of both longitudinal and transverse.
IV. Wave Function and Characteristics
A. Progressive Harmonic Wave
• A harmonic (sinusoidal) wave travelling along a string is an example of a
transverse wave. The medium as a whole does not move.
• General equation for a wave: y(x,t) = a \sin(kx \pm \omega t + \phi).
I. Introduction to Waves
• Waves are patterns that transfer energy without the actual physical matter as a
whole being transported.
• Waves transport energy and the pattern of disturbance from one location to
another.
• Not all waves require a medium for their propagation.
II. Types of Waves
A. Mechanical Waves
• Require a medium for propagation; cannot propagate through a vacuum.
• Involve oscillations of constituent particles and depend upon the properties of
the medium.
• Examples: Sound waves, water waves, seismic waves.
B. Electromagnetic (EM) Waves
• Do not necessarily require a medium; can travel in a vacuum.
• Examples: Light, radio waves, X-rays, etc..
• In a vacuum, all EM waves have the same speed (c).
C. Matter Waves
• Associated with constituents of matter (e.g., electrons, protons, molecules).
• Arise in quantum mechanical description.
• More complex than mechanical or EM waves.
• Used in a microscope.
III. Propagation of Sound Waves
A. Sound Waves in Air
• As the wave passes through air, it compresses or expands a small volume of air.
, • This causes a change in the density (\Delta\rho) and a corresponding change in
the pressure (\Delta p).
• The change in pressure induces a restoring force.
• The quantity similar to extension or compression of a spring is \Delta s.
• If a region is compressed, molecules are packed together, increasing density.
They tend to move out to the adjoining region, thereby rarefying the original
region.
• The rarefaction moves from one region to another, making compression and
rarefaction possible in air.
B. Sound Waves in Solids (Crystalline)
• Atoms are arranged in a lattice structure.
• Each atom is in equilibrium due to a force from surrounding atoms.
• Displacing one atom leads to restoring forces.
• Propagation of sound waves in fluids as well as solids can sustain compressive
strain.
• Transverse waves can only be propagated in media which can sustain shearing
stress, such as solids, but not in fluids.
C. Waves on Water Surface
• Capillary waves (Ripples): Short wavelength. Restoring force is produced due to
surface tension.
• Gravity Waves: Wavelength ranging from a few centimetres to several 100 m.
Restoring force is the pull of gravity which tends to keep the water surface at its
lowest level.
• Waves in the ocean are a combination of both longitudinal and transverse.
IV. Wave Function and Characteristics
A. Progressive Harmonic Wave
• A harmonic (sinusoidal) wave travelling along a string is an example of a
transverse wave. The medium as a whole does not move.
• General equation for a wave: y(x,t) = a \sin(kx \pm \omega t + \phi).
