What is a wave? A wave is the motion of a disturbance.

What is a wave? The medium is the physical environment through which a disturbance can travel. A mechanical wave is a wave that requires a medium. Some waves do not require a medium; electromagnetic waves are an example that we will study later.

Types of waves Pulse wave: A wave that consists of a single traveling pulse. Periodic wave: created by continuously generated pulses from one end of the rope.

Types of waves A wave whose source vibrates with simple harmonic motion is a sine wave.

Types of waves A transverse wave is a wave whose particles vibrate perpendicularly to the direction the wave is traveling. equilibrium

Wave Characteristics Crest: the highest point above the equilibrium position.

Wave Characteristics Trough: the lowest point below the equilibrium position.

Wave Characteristics Wavelength: the distance between two adjacent similar points of a wave crest to crest trough to trough

Wave Characteristics Amplitude: the maximum displacement from equilibrium. Crest to equilibrium Trough to equilibrium

Types of waves A longitudinal wave is a wave whose particles vibrate in parallel to the direction the wave is traveling.

Types of waves

Wave characteristics Wave speed

Wave characteristics Waves transfer energy The rate of that transfer depends on the amplitude at which the particles of the medium are vibrating. The greater the amplitude, the more energy the wave carries. Damping occurs when that energy diminishes over time. We disregard damping in many of our problems.

Wave characteristics The energy transferred is proportional to the square of the wave’s amplitude

Wave Interference Two waves can occupy the same space at the same time. The overlapping of two waves is called superposition.

Wave Interference Displacements in the same direction: constructive interference.

Wave Interference Displacements in opposite direction: destructive interference.

Wave Interference What happens when waves hit a boundary? Waves are reflected at a free boundary Waves are reflected and inverted at a fixed boundary.

Wave Interference A standing wave is a wave pattern that results when two waves of the same frequency, wavelength and amplitude travel in opposite directions and interfere. A node is a point in a standing wave that maintains zero displacement. An antinode is a point in a standing wave halfway between two notes at which the largest displacement occurs.

Sound Wave Production Sound waves are longitudinal. Compression: the region of a longitudinal wave in which the density and pressure are at a maximum. Rarefaction: The region of a longitudinal wave in which the density and pressure are at a minimum.

Sound Wave Production Sound waves are longitudinal because vibrations of air molecules are parallel to the direction of wave motion.

Sound Wave Production Tuning fork

Sound Wave Production Tuning fork

Sound Wave Characteristics Frequency (cycles per second) Low frequency = long wavelength High frequency = short wavelength

Sound Wave Characteristics Pitch: a measure of how high or low a sound is perceived to be, depending on the frequency of the sound wave.

Sound Wave Characteristics Sound can travel through solids, liquids or gases. Waves consist of vibrating particles. Sound travels much more quickly through a solid than a gas because the molecules are closer together.

Sound Wave Characteristics

Sound Wave Characteristics Sound speed depends upon the medium as we just saw. Sound speed also depends upon the temperature of the medium. As temperature increases, gas particles collide more frequently so sound can travel faster. Temperature has a negligible effect on liquids or solids.

Sound Wave Characteristics Sound waves propagate in three dimensions. We assume a spherical wave front for our purposes. Wave fronts ** Distance between wave fronts equals one wavelength

Standing Waves on a string

Standing Waves on a string Fundamental frequency: the lowest possible frequency of vibration of a standing wave.

Standing Waves on a string These frequencies form the harmonic series.

Standing Waves on a string Harmonic series: a series of frequencies that includes the fundamental frequency and integral multiples of the fundamental frequency.

Standing Waves on a string Harmonic series of standing waves on a vibrating string: ** Note: v is the speed of the waves on the string, not in the air.

Standing Waves in a pipe If both ends of the pipe are open, all harmonics are present. v = the speed of sound in the pipe L = length of pipe

Standing Waves in a pipe If one ends of the pipe is closed, only odd harmonics are present. v = the speed of sound in the pipe L = length of pipe

Standing Waves in a pipe Beat: the periodic variation in the amplitude of a wave that is the superposition of two waves of slightsly different frequencies.

Standing Waves in a pipe The number of beats per second corresponds to the difference between frequencies. Two flute players could use beats to tune their instrument. They would play the same note and one flute would be adjusted until no beats are heard, meaning the two flutes would be in tune.

Sound Intensity Intensity is the rate at which energy flows through a unit area perpendicular to the direction of wave motion.

Sound Intensity Intensity of a spherical wave:

Sound Intensity In combination, frequency and intensity determine which sounds are audible.

Sound Intensity Relative intensity: the ratio of the intensity of a given sound wave to the intensity at the threshold of hearing.

Sound Intensity There is a logarithmic dependence of perceived loudness on intensity. Loudness is measured according to a decibel level. A decibel is a dimensionless unit that is proportional to the log of a ratio using the threshold of hearing.

Sound Intensity Intensity (W/m2) Decibel Level (dB) Example 1.0x10-12 Threshold of hearing 1.0x10-11 10 Rustling leaves 1.0x10-10 20 Quiet whisper 1.0x10-9 30 Whisper 1.0x10-8 40 Mosquito buzzing 1.0x10-7 50 Normal conversation 1.0x10-6 60 Air conditioner at 6 m 1.0x10-5 70 Vacuum cleaner 1.0x10-4 80 Busy traffic 1.0x10-3 90 Lawn mower 1.0x10-1 110 Auto horn at 1 m 1.0x100 120 Threshold of pain 1.0x101 130 Machine gun 1.0x103 150 Jet plane

Resonance Natural frequency: the frequency at which a system tends to oscillate in the absence of any driving or damping force. Resonance: a phenomena that occurs when the frequency of a force applied to a system matches the natural frequency of vibration of the system, resulting in a large amplitude of vibration.

Resonance Natural frequency: the frequency at which a system tends to oscillate in the absence of any driving or damping force. Resonance: a phenomena that occurs when the frequency of a force applied to a system matches the natural frequency of vibration of the system, resulting in a large amplitude of vibration.