Waves Chapter 12

12-1 Simple Harmonic Motion Simple Harmonic Motion (SHM)- Any periodic motion that is the result of the restoring force that is proportional to the displacement. The mass-spring system and the simple pendulum are examples of SHM

Mass-Spring System Mass-spring system- A mass oscillating on a spring undergoes simple harmonic motion. Hooke’s Law Fspring = -kΔx Fspring = Force on the spring (N) K = spring constant (N/m) Δx = change in displacement (m) Fspring is negative because it always goes against the force applied to stretch or compress the spring

Simple Pendulum Simple pendulum- an object that swings back and forth. The object is called the bob. The restoring force is equal to the bob’s weight Simple pendulum works for small angles only (13≥θ≥0˚) θ = angular displacement = amplitude GPE increases as θ increases. Energy changes from GPE→KE→GPE →etc.

Simple Pendulum L= arm length Θ = amplitude T = tension forces mg = weight S = arc length

Time Period Time period (T)- the time it takes to complete one full cycle of SHM Mass-spring system 𝑇=2Π 𝑚 𝑘 m=mass k= spring constant T= time period for one full cycle Simple Pendulum 𝑇=2Π 𝐿 𝑔 L= Length g= gravity 9.81 m/s2 T= time period for one full cycle

Frequency Frequency-number of cycles that occur per time. Frequency units are Hertz (Hz) Hertz= 1 sec f = 1 T T = 1 f , frequency and time period are inverse of each other

12-3 Wave Properties Wave – motion of a disturbance Medium – material the disturbance travels through. The particles do not move with the wave. Mechanical Waves – waves that require a medium. Pulse Wave – a single pulse sent up and back Periodic Wave – repeated series of pulses.

Pulse Wave Periodic Waves

Parts of a Wave Crest – highest point Trough – lowest point Amplitude – maximum displacement Wavelength – distance traveled during one cycle(λ) Frequency(f) – number of cycles per time period. Period – time required for one complete vibration of particles in a medium Wave Speed: v=fλ

Parts of a Wave Period (seconds) time (meters)

12-3 Types of Waves Transverse Wave – particles of the disturbance move perpendicular to the wave motion. Ex. Baseball game wave Longitudinal Wave – particles of the disturbance move parallel to the wave motion. Ex. Sound wave, Density wave

Types of Waves

Types of Waves Longitudinal waves can also be called density waves. Compressed particles are under high density Stretched (rarefaction) particles are under low density. Density waves can be represented as a sine wave. Compressions are crests and rarefactions are troughs.

Wave Interference Constructive Interference – When two waves are added together and the resultant wave amplitude is larger. Destructive Interference - When two waves are added together and the resultant wave amplitude is smaller.

Wave Interference Constructive Interference Destructive Interference

Wave Reflection Reflection – The process of waves bouncing back. Fixed boundary – waves pulses will reflect inverted from its original position. Free boundary - waves pulses will reflect in its original position. Standing Wave – wave pattern consisting of pulses and reflected pulses, that does not appear to move along a medium. Only happens at certain frequencies. Nodes – points of complete destructive interference. Antinodes – points of complete constructive interference.

Reflection

Standing Wave 2 nodes, 1 antinode 3 nodes, 2 antinode N = Nodes A = Antinode 2 nodes, 1 antinode 3 nodes, 2 antinode 4 nodes, 3 antinode

Chapter 13 Sound Sound is a longitudinal wave. Frequency determines pitch. Wave speed depends on the medium. Faster in denser material. Ex. Speaking underwater. Infrasonic sound waves – low frequency (<20Hz) Range of human hearing 20Hz→20,000 Hz Ultrasonic sound waves – high frequency (>20,000Hz) An ultrasound is a procedure where high frequency sound waves are transmitted through a section of your body. Waves are partially reflected back during density changes. A sensor takes the reflected waves and makes an image. Ex. Pregnant woman

Ultrasound

Sound Waves Sound travels in 3-D Ex. Drop a rock in a pond S= Source of the disturbance λ S

Doppler Effect Doppler Effect- relative motion creates a change in frequency of a wave. The frequency is higher in the direction the source moves and lower when moving away. Lower λ, Higher f Lower λ, Higher f The Doppler Effect explains why sirens on emergency vehicles sound higher pitch when travelling toward you, but lower pitch while traveling away from you. The same process is used to track high density vs. low density clouds to predict storm movement. λ v λ S v = velocity of the source

Sound Intensity 𝑆𝑜𝑢𝑛𝑑 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦= 𝑃𝑜𝑤𝑒𝑟 𝐴𝑟𝑒𝑎 𝑆𝑜𝑢𝑛𝑑 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦= 𝑃𝑜𝑤𝑒𝑟 𝐴𝑟𝑒𝑎 𝑆𝑜𝑢𝑛𝑑 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦= 𝑃𝑜𝑤𝑒𝑟 4Π𝑟2 for a spherical wave Decibel Level – Sound intensity relative to the threshold of hearing

Sound Intensity

Resonance Resonance- the natural frequency of a material. Ex. Two identical tuning forks, same length pendulums, opera singer and a crystal glass, Tacoma Bridge

Homework Problems Chapter 12 Problems 1, 3-10, 12-13, 15-16, 18-22, 24-28, 30-32, 35-37, 39-45