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Transcript
Chapter 14: Vibrations and Waves & Chapter 15 : Sound Objects and Springs: One of the simplest types of ______________________ is an object attached to a _____________. An object attached to a spring obeys Hooke’s Law: Where x = displacement k = spring constant “-“ means the force is always in the opposite direction of the displacement In this case, the force on the spring is _______________________________to the amount of ________________________________. If the object is displaced ___________________ as much, it will feel a force ________ as strong pulling it back in the other direction. The restoring force is the force that _________________________________________ _____________________________________________________. An oscillation is the repetitive variation in time of the distance of the object from its equilibrium position. Oscillation of a Mass-Spring System Step 1: The spring is _________________ and released. Step 2: The spring ___________ the mass back _______________________. Step 3: The mass _________________ the equilibrium position. Step 4: The spring is ____________________. Step 5: The spring __________ the mass back ________________________. Step 6: and so on and so forth…. Simple Harmonic Motion Simple harmonic motion occurs when the _____________________________________ to the displacement from the equilibrium point and is always ______________________________ the equilibrium point. In other words, the net force obeys ____________________________. When two people play catch, does the ball have simple harmonic motion? Why? Does a mass-spring system turned on its side have simple harmonic motion? Why? Some Vocabulary _________________ (A): maximum displacement from equilibrium. _________________ (T): time it takes to execute a complete cycle of motion __________________(f): number of cycles or vibrations per unit of time o Unit: Hz = sec-1 Example: A spring is hung vertically and a ______kg object is attached to the lower end of the spring. When the mass is attached, the spring is stretched _____ cm. What is the spring constant? The Simple Pendulum A Simple Pendulum is a system that consists of a _________ attached to a light __________ that can __________ back and forth. A simple pendulum is a pendulum that swings at an ________________________. If it is swinging at more the 15o, it does not display simple harmonic motion. Equation for the period of a pendulum: A simple pendulum is suspended from the ceiling of a stationary elevator, and the period is measured. If the elevator moves with constant velocity, does the period (a) increase, (b) decrease, or (c ) stay the same? If the elevator accelerates upward, does the period (a) increase, (b) decrease, (c ) stay the same? Waves A wave is a disturbance that carries ________________ through __________________ or ____________________. Longitudinal Wave – Particles vibrate _________________ to the direction of the wave. Transverse wave – Particles vibrate __________________ to the direction of the wave. Defining Terms: _______________________ : maximum displacement from equilibrium. ________________________:time it takes to execute a complete cycle of motion ______________________:number of cycles or vibrations per unit of time (Hz = sec-1) ________________________: material through which a disturbance travels. ________________________: a wave whose propagation requires a medium. ________________________: a wave whose propagation does not require a medium. ________________________: a single non-periodic disturbance. ________________________: a wave whose source is some form of periodic motion. ________________________: wave pattern that results when two waves of the same f, , and A travel in opposite directions and interfere. WAVE ANATOMY: Draw and label compressions and rarefactions: Formulas are your friends: Sample Calculation 1 The string of a piano that produces the note middle C vibrates with a frequency of ________Hz. If the sound waves produced by this string have a wavelength in air of _____ m, what is the speed of sound in air? Sample Calculation 2 What is the period of vibration for an x-ray with a frequency of 3.0 x 1012 ______? Sample Calculation 3 A tuning fork produces a sound with a frequency of ______________ Hz. The speed of sound in water is ____________ m/s. Calculate the wavelength produced by this tuning fork in water. Wave speed depends on the _______________ in the string (F) and the _________________ (m) (mass of string per unit length) of the string Another Formula: Wave interactions/interference: ___________________________: any interference in which waves combine so that the resulting wave is bigger than the original waves. (Crest meets crest or trough meets trough) ___________________________: any interference in which waves combine so that the resulting wave is smaller than the largest of the original waves. (crest meets trough) ___________________________: a wave form caused by interference that appears not to move along the medium and that shows some regions of no vibration (nodes) and other of maximum vibration (antinodes). Picture of a standing wave: __________________________: when a wave bounces back off a boundary Label incident (incoming) and reflected waves. Free end reflection: Picture: Incident wave Reflected wave: Explanation: Fixed end reflection: Picture: Incident wave Explanation: Reflected wave: Chapter 15: Sound Sound waves are: _____________________ (requires a medium) ______________________ Draw a picture of a longitudinal wave; Label the compressions and rarefactions. Frequencies of Sound: Infrasonic Sound (elephants can hear) Audible Sound (humans can hear) Ultrasonic Sound (dolphins can detect) Pitch How high or low we perceive a sound to be, depending on the _______________ __________________________ As the frequency of a sound _______________, the pitch of that sound _______________. Images produced by __________________ show more detail then those produced with _____________________. Amplitude The _____________ of a sound wave corresponds with how ____________ the sound is. A ________________ amplitude is a _________________ sound. A ________________ amplitude is a _________________ sound. Practice: Draw a sound wave that is: 1) Loud and high pitched. 2)Loud and low pitched. 3) Quiet with medium pitch Speed of Sound in a medium: Sound travels fastest in _________________ because ___________________________ _______________________________________ and slowest in ______________ because ________________________________________________________________. Intensity & Decibel Level Sound waves propagate in 3D • Sound waves travel away from a vibrating source in all directions. • In these spherical waves, the circles represent compressions (wave fronts). __________ (I) of a wave is the rate at which _________ flows through a unit area (A) perpendicular to the direction of travel of the wave. • However, ___________ is also the rate at which ______________ is transferred (W = J/sec) • And sound waves are spherical, so the power is distributed over the surface area of a sphere (4r) I = Intensity (W/m2) P = Power (W) R = Distance from source (m) Example: What is the intensity of the sound waves produced by a trumpet at a distance of 3.2 m when the power output of the trumpet is 0.20 W? Human Hearing • The range of human hearing is generally considered to be from about ______ Hz to about 20,000 Hz. • In reality, it’s much worse. Few people can hear above 14-15 thousand Hz, and it gets worse as you grow older. • Hearing also depends on the ____________ of the sound. • The softest sound that can be heard by the human ear has an intensity of ________ W/m2. This intensity is said to be the ________________________. • The loudest sound the human ear can tolerate has in intensity of _____ W/m2. This is known as the Threshold of _______________. • When dealing with human hearing, the intensity range is very large (1x10-12W/m2 to 1W/m2). • A sound with twice the intensity isn’t heard as twice as loud. • The ear works on a logarithmic scale. Sound loudness is measured in ________________ (dB) which compare the sound’s intensity to the intensity at the threshold of hearing. Intensity Decibel (dB) Example • When the intensity is __________ (one -12 1x10 0 Threshold of hearing person talking vs two people talking) there -9 1x10 30 Whisper is a three decibel increase. -7 1x10 50 Normal Conversation • When the intensity is -4 ___________________ there is a ten 1x10 80 Traffic decibel increase and the noise sounds 1x10-2 100 Fire Engine __________ as loud. 1 1x10 120 Rock Concert • Example: A rather noisy typewriter -5 produces a sound intensity of 1 x 10 1x102 140 Jet 2 watts/m which is 70 dB. Find the decibel level when a second identical machine is added to the office. Calculating Decibel Level: = Decibel Level (dB) I = Intensity of the sound (W/m2) Io = 1 x 10-12 W/m2 Threshold of hearing Example: Ms. Koenig wants to install a 100. W stereo amp in her new VW. What will the dB level be at her ears which are approximately 1.5 m away from the speakers? Doppler Effect: The Doppler effect occurs because relative motion between the _______________ of waves and the ___________________ creates a change in ______________________. Pictures of the Doppler effect: How to calculate the change in frequency: fd = precieved frequency heard by the detector vd = velocity of the detector fs = frequency created by the source vs velocity of the source * Define the + direction to be v = velocity of sound from the source to the detector Doppler Effect Possibilities: Example: An ambulance moving at 25 m/s drives towards a physics student sitting on the side of the road. The EMTs in the ambulance hear the siren sounding at 650 Hz. What is the frequency heard by the student? (assume speed of sound is 343 m/s) Example: At rest a car’s horn sounds the note A (_________Hz). While the car is moving down the street, the horn is sounded. A bicyclist moving in the same direction with 1/3 the car’s speed hears a lower pitched sound. (A) Is the cyclist ahead of or behind the car? (B) If the car is moving at 33 m/s (with a horn frequency of 440 Hz) and the bike is following the car at 11 m/s, what is the frequency detected by the bicyclist? (assume speed of sound is 343 m/s) When an object is moving faster then the speed of sound it is called super sonic. The sound waves pile up behind the object creating a sonic boom. Picture of super sonic motion: Beats: When two different frequencies of sound are added together the resulting wave has varying amplitude. This varying amplitude is heard as beats. The frequency of the resulting beats can be calculated by: (two different frequencies) Example: A certain piano key is suppose to vibrate at 440 Hz. To tune it, a musician rings a 440 Hz tuning fork at the same time as he plays the piano note and hears 4 beats per second. What frequency is the piano emitting if the note the piano plays is too high? Beats can also occur from two sources playing the same frequency Examples: Constructive: Destructive: Example: Two speakers with the same frequency are placed 3.00 m apart. A listener is originally at point O, which is located 8.00 m from the center of the line connecting the two speakers. The listener then walks to point P, which is a perpendicular distance 0.350 m from O, before reaching the first minimum in sound intensity. What is the frequency of the speakers? (speed of sound in air is 343 m/s) Standing Waves & Resonance: The wave pattern that results when two waves of the same f,, and A travel in opposite directions and interfere. The ___________________ of the two waves appears to be ___________________. Resonance is the tendency of a system to vibrate with _________________ at a certain _________________. When a system is in resonance, a small input of _______________ leads to a ________________________________. Example: Blowing over a bottle of water will produce resonance. If the column of air in the bottle is ____ cm long, what is the resonant frequency of the bottle? (assume vsound = 343 m/s) • The water stops the sound so it is a node. • The air is free to move at the top of the bottle, so it is an antinode. • Going from node to the first antinode, is ¼ of a wave. • Therefore, the length of the bottle is ¼th the wavelength. Example: Resonance in a tube: Tuning fork with frequency of 958 Hz. What is the length (L) of tube out of the water? (Assume the speed of sound is 345 m/s.) Harmonics: • Sometimes more than one size wave will fit the given parameters. These different wave sizes are called _________________. • First harmonic (or fundamental frequency) is the ______________ wave that fits the parameters. • _____________ harmonic (first overtone) is the second largest wave that fits the parameters. Picture: 1st Harmonic: 2nd Harmonic: 3rd Harmonic: Types of Parameters: Tube with two open sides Example: 1st Harmonic: 2nd Harmonic: 3rd Harmonic: Tube one side closed Example: 1st Harmonic: 2nd Harmonic: 3rd Harmonic: String 2 fixed ends (tube, 2 closed ends) 1st Harmonic: 2nd Harmonic: 3rd Harmonic: Example: