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Chapter 11 Vibrations and Waves

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Elasticity When you hang a weight on a spring, the weight applies a force to the spring and it stretches in direct proportion to the applied force. According to Hooke’s law, the amount of stretch (or compression), x, is directly proportional to the applied force F. Double the force and you double the stretch; triple the force and you get three times the stretch, and so on: F ~ ∆x

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Elasticity If an elastic material is stretched or compressed more than a certain amount, it will not return to its original state. The distance at which permanent distortion occurs is called the elastic limit. Hooke’s law holds only as long as the force does not stretch or compress the material beyond its elastic limit.

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**Free Body Diagrams Revisited**

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**Spring force = - (spring constant) (displacement) Felastic = -kx**

Hooke’s Law Spring force = - (spring constant) (displacement) Felastic = -kx

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Hooke’s Law If a mass of 0.55 kg attached to a vertical spring stretches the spring 2.0 cm from its original equilibrium, what is the spring constant?

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**Simple Harmonic Motion**

Vibration about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium

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Simple Pendulums Amplitude Length Period Frequency

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Simple Pendulums

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Simple Pendulums At what position in the cycle of a swinging pendulum is the potential energy of the pendulum at a maximum?

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**Simple Harmonic Motion Calculations**

For a simple pendulum in simple harmonic motion For a mass-spring system in simple harmonic motion

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Waves Medium – a physical environment through which a disturbance can travel Mechanical wave – a wave that requires a medium to travel through Examples Non-examples

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Transverse Waves Wave motion is perpendicular to equilibrium

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Transverse Waves

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Transerve Waves

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Longitudinal Waves Wave motion is parallel to equilibrium

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**Wave Properties Pulse wave Reflection**

A wave that is just one interference – no repetition Reflection

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**Constructive and Destructive Interference**

Constructive interference A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave

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**Constructive and Destructive Interference**

A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave

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**speed of a wave = (frequency) (wavelength) v = f λ**

1. A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz. Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 m/s. 2. The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (3.00 x 108 m/s). Find the frequency of the laser light.

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De Broglie Waves Louis de Broglie suggested that all matter has wavelike characteristics. where h is Planck’s constant, equal to 6.63 x J·s. This wavelength is too small to notice interference for large objects. This idea becomes important when looking all things at the microscopic level.

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De Broglie Waves What is the wavelength of an electron (mass = 9.11 x 10¯31 kg) traveling at 5.31 x 106 m/s?

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Vibrations and Waves Chapter 11.

Vibrations and Waves Chapter 11.

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