Herriman High Honors Physics Chapter 11 Vibrations and Waves

Hooke’s Law Herriman High Honors Physics Practice A P. 371 Problems 2 & 4

Herriman High Honors Physics Simple Harmonic Motion  When a vibration or an oscillation repeats itself back and forth over the same path, the motion is said to be periodic.  The most common oscillation come from springs and you will recall from earlier chapters that the description of a spring’s oscillation requires some vocabulary.

Herriman High Honors Physics Oscillation of a Mass on a Spring Top picture is “rest position”; x = 0  Bottom picture is “stretched position” Here x represents the displacement. Maximum displacement is called the amplitude. One cycle refers to one complete to and fro motion. The period, T represents the time for one cycle. The frequency, f is the number of cycles in a given time period, usually one second.

Herriman High Honors Physics Relationship between Frequency and Period  Frequency – the number of cycles in one second  Period – the time required to complete one cycle.  Hence the relationship between period and frequency is: F = 1/T or T = 1/F  Where period is measured in seconds and frequency is measured in hertz (hz) which is 1/seconds.

Herriman High Honors Physics Sample Problem  A spring stretches m when a kg mass is attached to it. The spring is then stretched an additional 0.1 m from its equilibrium point and released. Find A) the spring constant K B) The amplitude of the oscillation C) The maximum velocity

Herriman High Honors Physics Solution  K = F/x = (.3 kg)(9.8 m/s 2 )/.150 m = 19.6 N/m  A =.1 m (can’t move further than where originally released, conservation of energy)  ½ mv 2 = ½ Kx 2 so

Herriman High Honors Physics Period of any Oscillating Body  From this equation we can derive an equation for the period of any oscillating body Which for the special case of a pendulum becomes:

Herriman High Honors Physics Sample Problem  A pendulum is 2 meters long. What is its period on earth where gravity is 9.8 m/s 2 ?  What would the period of the same pendulum be on the moon where gravity is 1.63 m/s 2 ?

Herriman High Honors Physics Solution On Earth On the moon Practice B P. 379 Problems 2 & 4 Practice C P. 381 Problems 1,3, & 5

Herriman High Honors Physics Waves  Waves are a form of periodic motion.  Two types of Waves (classified by movement) Transverse  Wave moves perpendicular to amplitude Longitudinal  Wave moves parallel to the amplitude Classified by medium Mechanical  Require a Medium Electromagnetic  Do not require a medium

Herriman High Honors Physics Wave Vocabulary  For a Transverse Wave Top – Crest Bottom – trough Wavelength (λ) – distance from crest to crest or trough to trough Frequency – number of waves or cycles per second Velocity – speed of wave

Herriman High Honors Physics Wave Vocabulary  For a Longitudinal Wave front – compression Back – rarefaction Wavelength (λ) – distance from compression to compression or rarefaction to rarefaction Frequency – number of waves or cycles per second Velocity – speed of wave

Herriman High Honors Physics The Wave Equation  By Definition V = fλ  Where v = wave velocity (meters/second) f = wave frequency (hertz) λ = wavelength in meters.

Herriman High Honors Physics Sample Problem  A boy sitting on a beach notices that 10 waves come to shore in 2 minutes. He also notices that the waves seem to be about 20 meters apart as they travel on the ocean. What is the frequency of the waves? What is the velocity of the waves?

Herriman High Honors Physics Solution  f = waves/second = 10/120 = hertz  V =fλ =(0.083 hz)(20 meters) = 1.66 m/s Practice D P. 387 Problems 2 & 4

Interference  When two waves pass through each other they are said to form an interference pattern according to the superposition principle.  To use this principle you superimpose the waves - draw one on top of the other, and look at the resulting wave pattern. Herriman High Honors Physics

Superposition Principle  There are two types of interference Constructive interference  Waves reinforce each other (a) Destructive interference  Waves cancel each other (b) Herriman High Honors Physics

Reflection at a boundary  Reflection at a fixed boundary are inverted. (a)  Reflection at a free boundary comes back upright. (b) Herriman High Honors Physics

Standing Waves  When a wave and its reflection reinforce in such a way that the result appears to be stationary, we call this a standing wave. In a standing wave the parts which destructively interfere or cancel are nodes and the parts which constructively interfere or reinforce are called anti- nodes. Herriman High Honors Physics

Standing Waves Herriman High Honors Physics