Chapter 9: Introduction to Waves Section 1: The Nature of Waves Section 2: Wave Properties The Behavior of Waves

Section 1: The Nature of Waves What is a wave? Wave – a repeating disturbance or movement that transfers energy through matter or space Waves carry energy without transporting matter from place to place A wave will travel only as long as it has energy to carry   Mechanical waves – waves that can only travel through matter Medium – the matter through which a mechanical wave can travel The medium can be either a solid, liquid, or gas Two types of mechanical waves: Transverse wave – the matter in the medium moves at right angles to the direction the wave is traveling example: a wave traveling through water Compressional wave – the matter in the medium moves parallel to the direction the wave is traveling example: a sound wave

Section 2: Wave Properties Describing Waves Amplitude Crests Troughs Wavelength rest position Characteristics of a Transverse Wave Compressions Rarefactions Wavelength Characteristics of a Compressional Wave

Section 2: Wave Properties Properties of Waves Wavelength () – distance between one point on one wave and the nearest point just like it on the following wave Units: distance units, usually meter Frequency (f) – how many wave lengths pas a fixed point each second Units: either /second (waves or cycles/second) or hertzs (Hz) Note: frequency is always reported in hertz (Hz), during math computations that unit is converted to /s (per second) Relationship between wavelength and frequency: as frequency increases, wavelength decreases Period (T) – time required for one wave to pass a fixed point Unit: second Relationship between period and frequency: the frequency of a wave is the inverse of the wave’s period, and vice-versa:

Section 2: Wave Properties Wave speed (v) – the product of wavelength and frequency Wave speed = wavelength x frequency, or: Example: a wave has a length of 0.25-m, and a frequency of 50-Hz. What is its speed? Solution Amplitude – a measure of the energy in a wave The greater the amplitude, the greater the energy In a compressional wave the amplitude is related to how tightly the particles in the medium are pushed together at the compressions and how far apart they in rarefaction In a transverse wave the farther the wave travels from the rest position the greater the amplitude λ = 0.25m f= 50.0 Hz = 50/s v= ? 𝑣=𝜆𝑓 𝑣=0.25𝑚 50 𝑠 𝒗=𝟏𝟐.𝟓 𝒎 𝒔

The Behavior of Waves Reflection – the bouncing back of a wave when it strikes a surface or boundary Reflection occurs when a wave strikes an object All waves can be reflected The Law of Reflection: The angle of the reflected wave is equal to the angle of the incident wave: Refraction – the bending of a wave when it travels from one medium to another The speed of the wave depends upon the medium through which it is traveling When a wave passes from one medium to another it changes speed The straw appears to bend because light waves travel faster in air than it does in water Reflecting Surface Normal Line Incident Wave Reflected i r Law of Reflection: =

The Behavior of Waves Diffraction – the change in the direction of a wave when an object causes the wave to bend around it Difference between diffraction and refraction: refraction occurs when waves pass through an object while diffraction occurs when waves pass around an object. Interference – the interaction between two or more waves that occupy the same space at the same time. There are two types:

The Behavior of Waves Constructive – the waves add together The amplitude of the new wave is equal to the sum of the amplitudes of the interfering waves Destructive – the waves subtract from each other as they overlap Occurs crest of one wave overlaps the trough of the second wave Standing wave – a wave pattern that forms when wave equal in wavelength and amplitude, but traveling in opposite directions, constructively interfere Nodes – points on a standing where the two waves cancel and no movement occurs Antinodes – points on a standing wave where movement is at a maximum Resonance – the ability of an object to vibrate by absorbing energy at its natural frequency In the case of sound waves, the sound gets louder Internet search: The Tacoma Narrows Bridge