CP Physics Chapter 12 Waves

Hooke’s Law F spring = kx During the periodic motion At equilibrium, velocity reaches a maximum (b) At maximum displacement, spring force and acceleration reach a maximum (a & c) A stretched or compressed spring has elastic potential energy.

Examples 1.A load of 45 N attached to a spring that is hanging vertically stretches the spring 0.14 m. What is the spring constant? 2.If a mass of 0.55 kg attached to a vertical spring stretches the spring 36 cm from its equilibrium position, what is the spring constant?

Measuring SHM  Amplitude (A) – the maximum displacement from equilibrium.  Period (T) –time it takes to complete one cycle, SI unit is seconds  Frequency (f) –how many complete cycles of motion in a unit of time, SI unit is hertz (Hz) f = 1/T

Simple Harmonic Motion

Examples 3.You are designing a pendulum clock to have a period of 1.0 s. How long should the pendulum be? 4.A mass of 0.30 kg is attached to a spring and is set into vibration with a period of 0.24 s. What is the spring constant of the spring?

Example #5 A 0.75 kg mass attached to a vertical spring stretches the spring 0.30 m. A.What is the spring constant? B.The mass-spring system is now placed on a horizontal surface and set vibrating. What is the period of the vibration?

Example #6 Calculate the period and frequency of a m long pendulum at the following locations: A) The North Pole, where g = m/s2 B) Chicago, where g = m/s2 C) Jakarta, Indonesia, where g = m/s2

SHM and Waves

Wave Parts  Amplitude  Time period  Wavelength – distance from same point to same point (i.e. peak to peak)  Crest – “peak”  Trough – “valley”

Wave Types  Pulse Wave: A single, non-periodic disturbance. If you hold a rope attached to a wall, you create a pulse wave if you give a single flip of your wrist.  Periodic Wave: A wave whose source is some form of periodic motion. If you move your hand up & down repeatedly, you produce a periodic wave

Wave Types  Transverse Wave: A wave whose particles vibrate perpendicularly to the direction of wave motion.

Wave Types  Longitudinal Wave: A wave whose particles vibrate parallel to the direction of wave motion.  This type of wave is also called a density or pressure wave. The crest areas are areas of high density or pressure called compressions. The troughs are areas of low density or pressure called rarefactions.

Important Truth About ALL Waves  Waves transfer ENERGY. Waves transfer energy by transferring motion, NOT by transferring matter. The rate at which a wave transfers energy depends on the AMPLITUDE at which the particles of the medium vibrate.

Example #7 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.

Example #8 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at 3.00 x 108 m/s. Find the frequency of the laser light.

Interference Constructive Interference Individual displacements on the same side of equilibrium are added together to form the resultant wave.

Interference Destructive Interference Individual displacements on opposite sides of equilibrium are added together to form the resultant wave.

Properties of Waves  Reflection

Standing Waves  A standing wave is the wave pattern that results when two waves of the same frequency, wavelength & amplitude travel in opposite directions and interfere.  Standing waves have nodes & antinodes. Node: undergoes total destructive interference & is therefore stationary. Node: undergoes total destructive interference & is therefore stationary. Antinodes: Half way between two nodes. Total constructive interference and therefore the point of the largest amplitude. Antinodes: Half way between two nodes. Total constructive interference and therefore the point of the largest amplitude.

Standing Waves

Example #9 A wave of amplitude 0.30 m interferes with a second wave of amplitude 0.20 m. What is the largest resultant displacement that may occur?

Example #10 A string is rigidly attached to a post at one end. Several pulses of amplitude 0.15 m sent down the string are reflected at the post and travel back down the string without a loss of amplitude. What is the amplitude at a point on the string where the maximum displacement points of two pulses cross? What type of interference is this?

Example #11 How would your answer to problem 2 change if the same pulses were sent down a string whose end is free? What type of interference is this?