Chpater 15 Mechanical Waves
Chpater 15 Mechanical Waves
Chpater 15 Mechanical Waves
Waves
Earthquake waves
carry enormous
power as they travel
through the earth.
Other types of
mechanical waves,
such as sound waves
or the vibration of the
strings of a piano, carry far less energy.
Overlapping waves interfere, which helps us understand musical instruments.
For a periodic wave, each particle of the medium undergoes periodic motion.
The wavelength, λ, of a periodic wave is the length of one complete wave pattern.
The speed of any periodic wave of frequency f is v = λf
The particles move up and down, but the wave moves to the right.
Wave that results is a symmetrical sequence of crests and troughs.
Sinusoidal Waves - periodic waves with simple harmonic motion
When a sinusoidal wave passes through a medium, every particle in the medium undergoes
Wave Motion is the movement of wave with constant speed along the length of the string,
while Particle Motion is simple harmonic and transverse (perpendicular) to the length of the
string.
Particles oscillate back and forth along the same direction that the wave moves
SHM of longitudinal wave forms regions in the fluid where the pressure and density are greater
or less than the equilibrium values. Compressions are region of inceased density while
Rarefactions are regions of decreased density.
Each particle in the fluid oscillates in SHM parallel to the direction of wave propagation with the
same amplitude A and
period T
15.3. Mathematical
Description of Wave
The wave
function, y(x,t), gives a
mathematical description
of a wave. In this
function, y is the
displacement of a particle at time t and position x.
Phase differences - differences in cyclic motions of various points on the string are out of step
with each other by various fractions of a cycle.
The wave function for a sinusoidal wave moving in the +x-direction are:
where k = 2π/λ is called the wave number
(kx ± ωt) called the phase, plays the role of an angular quantity (always measured in radians)
15.4. Speed of a
Transverse Wave
Speed of
transverse
waves is
affected by tension in the string and its mass per unit length (also called linear mass density).
Tension
F = mg
Speed of Mechanical Waves
15.5. Energy in Wave Motion
Wave Intensity
time average rate at which energy is transported by the wave, per unit area
The intensity I at any distance r is therefore inversely proportional to r².This relationship is called
the inverse-square law for intensity.