VIBRATIONS AND

WAVESChapter 14

Section 1: Periodic Motion

Periodic motion: A repeating regular cycleExample: The moving up and down of a pendulum

Equilibrium vs. Non-zero position

a. c.

b.

Period: Time needed for an object to complete 1 cycle of motion

Simple Harmonic Motion: Force acting directly proportional to the displacement of the objects in order to restore the object’s equilibrium.

Hooke’s law: the force exerted by a spring is directly proportional to the amount that the spring is stretched. NOTE: The negative sign in the Hooke’s Law constant indicates a force opposite the stretch of compression

Elastic Potential Energy: Stretching a spring gives it a potential energy. The longer it stretches, the higher is its potential energy.

A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended from its end.

PROBLEM SOLVING

a. Determine the spring constant.b. How much elastic potential energy is stored in the

spring when it is stretched this far?

Periodic Motion

Known:

x = 18 cm

F = 56 N

Unknown:

k = ?

PEsp = ?

a. Spring constant

F = −kx

b. EPE

Period of a pendulum: also a good example of a harmonic motion.

A simple pendulum consists of a bob, suspended by a string or light rodNOTE: Period of a pendulum depends of the length and g no the mass of the bob and the amplitude of oscillation

Resonance: Small forces applied at regular intervals to an oscillating or vibrating objects and the amplitude of the vibration increases.

Sample Problem, Page 387

A pendulum with a length of 36.9cm has a period of 1.22 s. What is the gravitational field at the pendulum’s location?

Sample Problem, Page 387A pendulum with a length of 36.9cm has a period of 1.22 s. What is the gravitational field at the pendulum’s location?

Section 2: Wave Properties

Wave: a disturbance that carries energy through matter or space

Mechanical wave: a wave that travels to a physical medium (air, water or solid objects)

Electromagnetic wave: a wave that can travel even without a medium

1. Transverse wave: vibrates perpendicular to the direction of the wave’s motion.2. Longitudinal wave: transition from compression and rarefaction.

Types of Mechanical wave

Types of Mechanical wave3. Surface wave : which has characteristics of both transverse and longitudinal waves.

Wave Properties1. Wavelength: Shortest distance between 2 points where the wave patterns repeats itself

Wave Properties2. Speed: How fast the wave is travelling

v = ∆d /∆t.

Note: Speed depends only on the medium through which waves move.

Wave Properties3. Amplitude: the maximum displacement of the wave from its position of rest or equilibrium

Note: More work must be done to generate a wave with a greater amplitude. Waves with greater amplitudes transfer more energy.

Wave Properties4. Phase:

Any two points on a wave that are one or more whole wavelengths apart are in phase.

Particles in the medium are said to be in phase with one another when they have the same displacement from equilibrium and the same velocity.

Particles in the medium with opposite displacements and velocities are 180° out of phase.

Two particles in a wave can be anywhere from 0° to 180° out of phase with one another.

Wave Properties5. Period: Time required an object to repeat one complete cycle motion

6. Frequency: Number of complete oscillations a part on a wave makes each second

Problem solving, page 392A sound wave has a frequency of 192 Hz and travels the length of a football field, 91.4m, in 0.271s.a. What is the speed of the wave?b. What is the wavelength of the wave?c. If the frequency were changed to 442 Hz, what

would be the new wavelength and period?

Problem solving, page 392

a. What is the speed of the wave?

Problem solving, page 392b. What is the wavelength of the wave?

Problem solving, page 392c. If the frequency were changed to 442 Hz, what would be the new wavelength and period?

Section 3: Wave Behavior

Incident wave: pulse that strikes the boundaryReflected wave: returning wave

Rigid Boundary: Reflection may be inverted because the other spring is stiffer

Principle of superposition: The algebraic sum of two or more waves forming a new waveInterference: result of the superposition of two or more waves.

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Standing waves: A wave that appears to be standing still

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Waves in two dimensions

Wave front: A line that represents the waves in two dimensionsRay: Direction of the wave (right angle to the wave front)

Two dimensional waves (ripple tank experiment)

Law of reflection: the angle of incidence is equal to the angle of reflection

Refraction: Change in the direction of waves at the boundary between two different mediums

HOMEWORK

Choose ONE of the following. Make a very brief discussion on how your chosen topic below is related to vibrations and waves. Limit your output to a maximum of 100 words. You can email your output to teresa@iasdubai.com. Or you can write or encode it on any sheet of paper.1. Tsunamis 2. Earthquake resistant building