Foundations of Physical Science Unit 4: Sound and Waves

Chapter 12: Waves 12.1 Waves 12.2 Waves in Motion 12.3 Natural Frequency and Resonance

Learning Goals Learn the role waves play in our daily lives, including our effort to communicate. Learn the parts and shapes of waves. Model transverse and longitudinal waves and their characteristics with a stretched string. Explore the properties of waves (like reflection and diffraction) with water. Investigate resonance and harmony using an electronic synthesizer. Learn how natural frequency and resonance are involved in making music.

Vocabulary circular waves continuous harmonics constructive interference crest hertz destructive interference diffraction fundamental plane longitudinal wave natural frequency reflection refraction resonance response transverse wave trough standing wave wave fronts waves

Why learn about waves? Waves carry information and energy over great distances Anytime you see a vibration that moves Sound waves Radio waves Microwaves The information could be sound, color, pictures, commands, or many other useful things

Transverse Waves The direction of the wave travel is perpendicular to the direction of the vibrating source Examples: Stringed instruments Water waves Electromagnetic waves

Longitudinal Waves The direction of the wave is along the direction in which the source vibrates Example: Shake a slinky back and forth

Frequency, Amplitude, & Wavelength Waves have cycles, frequency, and amplitude, just like oscillations Frequency: how often the wave goes up and down; measured in hertz Amplitude: the largest amount that goes above or below average; ½ distance between the highest and lowest places

Frequency, Amplitude, & Wavelength Wavelength: the length of one complete cycle of a wave Crest-to-Crest Trough-to-Trough Represented by lambda λ

Wave Speed How fast the wave can transmit an oscillation from one place to another Water waves are slow; a few mph Sound waves are fast; 660 mph Light waves are very fast; 186,000 mph How quickly a movement of one part of the water surface is transmitted to another place Start a ripple in one place and measure how long it takes the ripple to affect a place some distance away

Wave Speed Wave speed = wavelength/period Wave speed = wavelength X frequency The speed of a wave is related to the frequency and wavelength of the waves Example: wavelength =10 m Time between crests at a point on the surface = 0.5 s The wave moves 10 m / 0.5 s, or 20 m/s

Wave Speed In one complete cycle, a wave moves forward one wavelength

Example If a water wave vibrates up and down 3 times each second and the distance between wave crests is 2m, what is the: (a) wave’s frequency? (b) wavelength? (c) wave speed? (a) 3 Hz (b) 2m (c) wave speed = frequency x wavelength = 3/s x 2 m = 6 m/s

Wave Shapes Crest: the highest points of the wave Wave fronts: another name for the crests of the wave Wave shapes are determined by the wave fronts Trough: the lowest points of the wave

Wave Shapes Plane waves: the crests look like straight lines; waves move in a line perpendicular to the wave fronts Circular waves: the crests are circles; waves move outward from the center

What Happens When A Wave Hits Something? Reflection Refraction Diffraction Absorption Boundaries: waves are affected by boundaries where conditions change

Natural Frequency A frequency at which an elastic object naturally tends to vibrate Minimum energy is required to produce a forced vibration or to continue vibration at that frequency

Natural Frequency The natural frequency depends on many factors, such as tightness, length, or weight of a string We can change the natural frequency of a system by changing any of the factors that affect the size, inertia, or forces in the system Tuning guitar changes the natural frequency of a string by changing its tension

Natural Frequency All things in the universe have a natural frequency, and many things have more than one. If you know an object’s natural frequency, you know how it will vibrate. If you know how an object vibrates, you know what kinds of waves it will create. If you want to make specific kinds of waves, you need to create objects with natural frequencies that match the waves you want

Resonance The natural frequency of the system exactly in tune with the force applied Something is vibrated at its natural frequency

Resonance Examples Calvary troops marching across a footbridge in England in 1831 caused a bridge to collapse when they marched in rhythm with the bridge’s natural frequency! Troops must “break step” when crossing bridges 1940 collapse of the bridge across the Tacoma Narrows in Washington Four months after being built the bridge was destroyed by wind-generated resonance

Standing Waves A stationary wave pattern formed in a medium Two sets of identical waves pass through the medium in opposite directions The effect of waves passing through each other

Standing Waves Positions of zero rope displacement in a standing wave are called nodes At each end of any loop there is a node, and two loops make one wavelength Distance between adjacent nodes is one-half wavelength

Standing Waves on a String A wave trapped in one spot A vibrating string; makes music on a guitar or piano Standing waves occur at frequencies that are multiples of the fundamental Fundamental: the natural frequency of the string Harmonics: the fundamental and multiples of its frequencies

Standing Waves on a String A vibrating string moves so fast that your eye averages out the image and sees a wave-shaped blur We can control standing wave frequencies and wavelengths We can increase amplitude

Interference The result of superimposing two or more waves of the same wavelength

Interference Constructive Interference: occurs when waves add up to make a larger amplitude Destructive Interference: occurs when waves add up to make a smaller amplitude

Constructive Interference Crest-to-crest reinforcement

Destructive Interference Crest-to-trough cancellation

Example Is it possible for one wave to cancel another so that no amplitude remains? Yes. This is destructive interference. In a standing wave in a rope, for example, parts of the rope-the nodes-have no amplitude because of destructive interference.