Phys Chapter 9 Waves

H Notes Ch 9 ­ Waves (1).notebook Period (T): ­ Units are seconds (s) The time required to complete one cycle. Honors Physics Lesson 9.1 Periodic Motion Frequency (f): ­ Units are hertz (Hz) (1 Hz = 1 wave / s or 1 vibration / s) The number of cycles the object completes per second. Remember: The period and frequency are reciprocals. Pendulum: A pendulum is one example of Simple Harmonic Motion.: Let's see if we can figure out what factors determine the period (and frequency) of a simple pendulum. Simple harmonic motion is motion in which the restoring force is proportional to the displacement. Another simple example is a mass bouncing at the end of a spring. Note that the period is, surprisingly, not dependent on the amplitude of the vibrations. Amplitude (A) is the maximum displacement the object achieves from its equilibrium position. Honors Physics Lesson 9.2 Waves Basics Vibration ­ A wiggle in time * Wave ­ A wiggle in space and time * A wave transfers energy from one location to another. Two types of waves: Mechanical waves (like small water waves) are a transfer of kinetic energy caused by a vibrating object. Mechanical waves require a medium to travel through. "Medium" is basically a fancy term for the substance that vibrates to carry the kinetic energy. Electromagnetic waves (like light) are a transfer of electromagnetic energy caused by vibrating electric charges. Electromagnetic waves are unique because they do not require a medium to travel through and so they can travel through a vacuum. Transverse v. Longitudinal Waves A transverse wave is a wave in which the direction the particles vibrate in is perpendicular to the direction the wave's energy is traveling in. Examples: Small water waves The wave at a stadium A longitudinal wave (also called a "compression wave") is a wave in which the direction the particles vibrate in is parallel to the direction the wave's energy is traveling in. Examples: Sound waves Wavelength (λ): ­ Units are meters (m) The distance between two successive crests, troughs, or identical points on a wave. Amplitude (A): ­ Units are meters (m) This is the maximum displacement of a particle's vibration...it's half of the distance the particle goes back­and­forth. (People often say "amplitude is the height of a crest"...this is fine for transverse waves, but doesn't help us understand amplitude of longitudinal waves.) Amplitude is determined by the size of the particle's vibrations. If all other things are constant, a larger amplitude means the wave is carrying more energy. Period (T): ­ Units are seconds (s) The time required for the vibrating source of a wave to complete one vibration. ­­­­or­­­­ The time required for one particle in the wave's medium to complete one vibration. ­­­­or­­­­ The time required for a wave to travel a distance of one wavelength. The period is determined by how quickly the wave's source is vibrating Frequency (f): ­ Units are hertz (Hz) (1 Hz = 1 wave / s or 1 vibration / s) The number of vibrations the source of a wave completes per second. ­­­­or­­­­ The number of vibrations one particle in the wave's medium completes in one second. ­­­­or­­­­ The number of wavelengths the wave travels per second. The frequency is determined by how quickly the wave's source is vibrating Remember: The period and frequency are reciprocals. Wave Speed or Wave Velocity (v): The rate at which a wave's energy moves. A wave's speed is determined by the medium it travels through. For example, the rate at which sound travels depends on the medium it travels through. Please don't make the mistake of thinking that as the frequency increases, the velocity increases. NO! As the frequency increases, the wavelength decreases. The velocity does not change unless the medium the wave is traveling in changes! Example: Frank makes a water wave in the bath tub by tapping the water twice per second. The resulting waves are 0.25 m apart. a. Find the velocity of the waves. b. How far apart would the waves be if he tapped the water five times per second? Honors Physics Lesson 9.3 Sound Waves A sound wave is caused by a vibrating source. The vibrations of this source cause the medium it is in to vibrate. These vibrations emanate outward from the source in concentric circles. As the vibrations move, they may eventually reach your ears causing your ear drums to vibrate. Your brain then interprets these vibrations as sound. As is the case with any other wave, the velocity of a sound wave is determined by the medium it travels through. Sound is a longitudinal wave! The pitch of a sound wave is determined by the frequency of its vibrations. Humans can hear sounds between about 20 Hz and 20,000 Hz. • A sound which has a frequency of more than 20,000 Hz is called ultrasonic. • A sound which has a frequency of less than 20 Hz is called infrasonic. Unrelated, but similar words are: Supersonic which is used to describe an object which is traveling faster than the speed of sound. Subsonic which is used to describe an object which is traveling slower than the speed of sound. The volume of a sound wave is determined by the amplitude of its vibrations. We can measure volume two different ways: The intensity of a sound wave varies inversely with the square of the distance from the source. So if you stand 6 meters away from an air conditioning unit, the sound you'll hear will have an intensity of 1.0 * 10­6 W / m2. Find the intensity if you stand: a. 2 m away b. 12 m away Forced Vibration: This occurs any time the vibrations of one object force another object to vibrate. Examples: • Vibrations of a speaker cone force the air to vibrate • Vibrations of a guitar string forces the body of guitar to vibrate • Vibrations of a water wave force the sand to vibrate • Vibrations of a water wave force a floating duck to vibrate • Vibrations of air molecules from a thunder clap force water in a glass to vibrate Honors Physics Lesson 9.4 Resonance Natural Frequency (AKA Fundamental Frequency): If an object is pushed or pulled, very briefly, by an external force, it will vibrate at a frequency called its natural frequency. Examples: • Pushing a kid on a swing • Plucking a stringed instrument • Dropping an object Resonance: This occurs when the frequency of a forced vibration matches an object's natural frequency. The result is the amplitude of the object's vibrations are increased. Examples: • Pushing a kid on a swing • Pumping on a swing • Breaking a wine glass with your voice • Rocking a car out of the mud Honors Physics Lesson 9.5 Boundaries and Standing Waves Boundary: When a wave travels from one medium to another, we say the wave has encountered a "boundary." At this point, at least one of two things will happen: Standing waves: When a wave travels through a medium of a fixed length, sometimes the incident and reflected waves interfere in a way that gives the illusion of the wave "standing" in place. The frequencies for which this occurs are called "Harmonics." Reflection Some of the wave's energy bounces back in the original medium. How these standing waves look depends on the boundaries of the medium...if they are "fixed" or "loose." Refraction Some of the wave's energy continues on into the new medium and experiences a corresponding change in speed. In both cases, the frequency is unchanged! Standing waves in a string usually have two fixed ends (like on a stringed instrument). And since the velocity of the wave is determined by the properties of the string, we see that these wavelengths determine the frequencies of each harmonic. Sometimes a medium has two loose ends. This usually occurs in a column of air. Once again, the velocity of the wave determines the frequency of each harmonic. Sometimes a medium has one fixed end and one loose end. This may occur in a string or column of air opened at one end. Once again, the velocity of the wave determines the frequency of each harmonic. Honors Physics Lesson 9.6 The Doppler Effect This can be a bit tricky because there are three different velocities: vwave = vw : vsource = vs : This is the velocity that the wave travels at. This is the velocity of the object which is creating the waves. Examples: This might mean the velocity of... A boat moving through water making water waves A jet moving through air making sound waves A sun moving through space making light waves vobserver = vo: This is the velocity of the object which is hearing, seeing, or experiencing the waves. Examples: This might mean the velocity of... A person in an inner tube being hit by the boat's waves A person on the ground hearing the jet fly over head A person on a planet looking at the sun This means there are also two frequencies: fs = the frequency of the wave the source creates Example: The frequency at which the boat creates water waves The frequency of the sound created by the jet The frequency of the light created by the sun fo = the frequency the observer experiences The frequency at which the person in the inner tube gets hit by the boat's waves The frequency at which the person on the ground gets hit by compressions from the jet's sound waves The frequency at which the person on the planet gets hit by the light wave's vibrations. The Doppler Effect occurs when either the source or the observer are moving. The result is the observer will experience a different frequency than the source is producing. Moving Source, Stationary Observer....Here the source is moving MUCH slower than the wave. Moving Source, Stationary Observer....Here the source is moving a even faster and only a little bit slower than the wave. Moving Source, Stationary Observer....Here the source is moving a little faster than the last one but still slower than the wave. Notice...any time the observer and source are moving toward each other, the observer will experience a frequency which is HIGHER than the frequency the source is creating. fo > fs Notice...any time the observer and source are moving apart from each other, the observer will experience a frequency which is LOWER than the frequency the source is creating. fo < fs Honors Physics Lesson 9.7 Bow & Shock Waves Moving Source, Stationary Observer....Here the source is moving a little bit faster than the wave. Moving Source, Stationary Observer....Here the source is moving a little bit faster than the wave. Moving Source, Stationary Observer....Here the source is moving WAY faster than the wave. Once the source starts moving as fast as the wave, or faster than the wave, we still get the Doppler effect, but more importantly we get constructive wave interference which results in a Bow Wave or Shock Wave. If the source is creating waves that spread in 2­ dimensions (like waves on the water surface) we get a Bow Wave. If the source is creating waves that spread in 3­ dimensions (like sound waves or light waves) we get a Shock Wave. Moving Source, Stationary Observer....Here the source is moving a lot faster than the wave.