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Chpater 15 Mechanical Waves

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Chapter 15: Mechanical

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.

15.1. Types of Mechanical Waves

 Mechanical Wave - a disturbance traveling through a medium


 Transverse Waves - displacement of the medium are perpendicular to the direction of travel of
the wave
 Longitudinal Waves - displacement of the medium are parallel to the direction of the wave
travel; time the motions of the particles of the medium are back and forth along the same
direction that the wave travels
 Surface Waves/ Complex Waves - dsiplacement of water have both longitudinal and transverse
components, ended up moving in a circle
 Wave speed/ speed of propagation - definite speed in which a wave travels or propagate
through a medium

Mechanical Waves Requirements

 Some source of disturbance


 A medium containing elements that can be disturbed
Some physical mechanism through which elements of the medium can influence each other

15.2. Periodic Waves - wave propagation is in repetitive or periodic motion

 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 = λf

Periodic Transverse Waves

 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

simple harmonic motion with the same frequency

 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.

Periodic Longitudinal Waves

 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)

Particle Velocity and Acceleration

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

Power in Wave Motion (maximum)

Power in Wave Motion (average)

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.

15.6 Wave Interference, Boundary Conditions, and Superposition

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