1) Below is a standing wave

 1) Below is a standing wave. It is being vibrated at 80 Hz. a. What is the harmonic that it is vibrating in? 2nd (read off graph) b. What is the wavelength of that harmonic? 30 m (read off graph) c. What is the speed of the wave on the string? v = f* wavelength= 2400 m/s d. What is the fundamental or first harmonic frequency? fn = n* f: f = fn/n: f=80/2=40 Hz e. What is the wavelength of the first harmonic? wavelength= v/f =2400 m/s /40 Hz = 60 m f. What is the amplitude of this wave? 10 cm (read off graph) 2. There are two diagrams below,. One with respect to time and one with respect to distance (camera picture) a. Give the value of the period (include units). 30 s (read off top graph) b. Give the value of the wavelength (include units). 30 m (read off bottom graph) c. Give the value of the amplitude (include units). 10 cm (read off either graph) d. Find the frequency. f= 1/T =1/(30 s) = .033 Hz e. Find the velocity. v = wavelength / T = 30 m/ 30 s = 1 m/s f. Draw a wave on either diagram that would completely cancel (destructive interference) the wave shown. Be careful to make sure that your sketch is precisely drawn. To completely cancel your wave should be the opposite (a maximum where there was a minimum and the same amplitudes) of the original. g. On the other hand, if you were asked to have them add constructively instead – you would have to draw a wave that was positive when the original was positive and negative when the original was negative. 12 10 8 displacement (cm) 6 4 2 0 -2 -4 -6 -8 -10 -12 0 15 distance (meters) 30 Vibrations and Waves ? ? ? A vibration is a wiggle in time A wave is a wiggle in both time and space Both sound and light travel in waves ? Sound is the propagation of vibrations through a solid, liquid, or gas ? ? Cannot travel in a vacuum Light is the vibration of electric and magnetic fields– a vibration of pure energy ? Can travel through medium and vacuum Vibration of a Pendulum Period – the time it takes for a pendulum to swing to and fro ? The period is dependent only on the length of the pendulum and the acceleration of gravity ? ? Drop – same g; Incline – same fraction of g; Pendulum same length – same period Wave Description ? ? Sine curve – waveform traced by simple harmonic motion Frequency – number of vibrations per unit time (I.e. number of crests that pass per unit time) Frequency = 1/period ? Units: Hertz (Hz) which are vibrations per second ? ? Period – the time in which a vibration is completed ? Period = 1/frequency Wave Motion ? Wave motion can be seen as a rhythmic disturbance in a medium where every portion of the medium is impacted as the disturbance flows along the medium, and then it returns to normal ? Examples: rope, surface of water, grass, etc. Wave Speed Wave speed = wavelength/period ? Wave speed = wavelength x frequency ?V=fl ? Transverse Waves Transverse waves – motion of the medium is transverse (90 degrees) to the direction the wave travels ? Examples: stretched stringed instruments, surface of liquids, electromagnetic waves ? Longitudinal Waves ? ? ? ? Longitudinal waves produce motion along the direction of the wave (push-pull type motion) Wave of compression travels along the medium The stretched regions are called rarefaction Sounds waves are longitudinal waves Interference Superposition principle – when more than one wave occupies the same space and time the displacements add at every point ? Constructive interference occurs when the waves add to result in an increased amplitude ? Destructive interference occurs when the high part of one is added to the low part of the other canceling each other out. ? Standing Waves ? A stationary wave pattern formed in a medium when two sets of identical waves pass through the medium in opposite directions ? Examples: strings of musical instruments, as well as clarinets, trumpets, organ pipes, etc. ? Can be produced by either transverse or longitudinal vibrations Doppler Effect ? ? The change in frequency due to the motion of the source (or receiver) Can be heard in the change of pitch of an approaching ambulance, where the pitch is higher as it approaches and lower after it passes you Bow Waves The V-shaped disturbance created by an object moving across a liquid surface at a speed greater than the wave speed ? Examples: A speed boat knifing through the water ? Shock Waves ? The cone-shaped disturbance created by an object moving at supersonic speed through a fluid. ? Actually two cones, one highpressure, and one low ? Sonic boom– the loud sound resulting from the incidence of a shock wave ? The sudden increase in pressure is much the same in effect as the sudden expansion of air produced by an explosion. Example Problem 1 ? What is the frequency, in hertz, that corresponds to each of the following periods? (a) 0.10 s, (b) 5 s, (c) 1/60 s. ? Answer: ? (a) f = 1/T = 1/0.10 s = 10 Hz; ? (b) f = 1/5 = 0.2 Hz; ? (c) f = 1/(1/60) s = 60 Hz. Example Problem 2 ? A skipper on a boat notices wave crests passing his anchor chain every 5 s. He estimates the distance between wave crests to be 15 m. He also correctly estimates the speed of the waves. What is this speed? ? Answer: ? The skipper notes that 15 meters of wave pass each 5 seconds, or equivalently, that 3 meters pass each 1 second, so the speed of the wave must be ? Speed = = = 3 m/s. ? Or in wave terminology: ? Speed = frequency ? wavelength = (1/5 Hz)(15 m) = 3 m/s. Example Problem 3 ? Radio waves travel at the speed of light – 300,000 km/s What is the wavelength of radio waves received at 100.1 MHz on your FM radio dial? ? Answer: ? To say that the frequency of radio waves is 100 MHz and that they travel at 300,000 km/s, is to say that there are 100 million wavelengths packed into 300,000 kilometers of space. Or expressed in meters, 300 million m of space. Now 300 million m divided by 100 million waves gives a wavelength of 3 meters per wave. Or ? speed (300 megameters/s) Wavelength = = = 3 meters frequency (100 megahertz) Example Problem 4 ? On a keyboard, you strike middle C, whose frequency is 256 hz. (a) What is the period of one vibration of this tone? (b) As the sound leaves the instrument at a speed of 340 m/s, what is its wavelength in air? ? Answer: ? (a) Period = 1/frequency = 1/(256 Hz) = 0.00391 s ? (b) Speed = wavelength ? frequency, so wavelength = speed/frequency = (340 m/s)/(256 Hz) = 1.33 m. Example Problem 5 ? The wavelength of the signal from TV Channel 6 is 3.42 m. Does Channel 6 broadcast on a frequency above or below the FM radio band, which is 88 to 108 MHz? ? Answer: ? Below. ? Speed = frequency ? wavelength, so frequency = speed/wavelength = (3 ? 108 m/s)/(3.42 m) = 8.77 ? 107 Hz = 87.7 MHz, ? just below the FM band. Sound Most sounds are produced by the vibrations of material object ? Frequency corresponds with pitch ? High pitch – high frequency (piccolo) ? Low pitch – low frequency (foghorn) ? ? Hearing limits young people: 20-20,000 Hz ? older people: smaller range especially at high end ? Infrasonic – frequencies below 20 Hz ? Ultrasonic – frequencies above 20,000 Hz ? Nature of Sound in Air ? Sound travels as longitudinal waves ? ? Made up of a series of compressions and rarefactions It is not the medium itself that travels, but the energy carrying pulse. Media that transmit sound ? Any elastic substance can transmit sound ? Elasticity is the ability of a material to deform (reversibly) in response to a force ? Sound travels: ? ~4X faster in water than air ? ~15X faster in steel than air Speed of Sound in air ? Dependent upon: ? Wind conditions, temperature, and humidity Speed of sound in dry air (0ºC) is ~330 m/s ? Humidity & heat increase the speed of sound ? For each degree above 0ºC, the speed increases by 0.6 m/s ? At R.T., (20ºC), sound travels at ~ 340 m/s ? Reflection of Sound ? ? ? ? ? An echo is the reflection of a sound The fraction of energy carried by the echo is: ? large if the surface is rigid and smooth ? less if soft and irregular If surface is too reflective, sound is garbled due to reverberations If surface is too absorbent, the sound level will be low, and will sound dull and lifeless Concert halls place reflective surfaces behind the stage to direct sound out to the audience Refraction of Sound ? ? ? ? Refraction - Sound waves bend when parts of the wave front travel at different speeds On a warm day, the air near the ground is warmer, causing sound to bend away from the ground On a cool day, the air near the ground is colder, sound bends toward the ground, causing sound to travel farther over long distances. Ex: submarines, ultrasound, dolphins Energy in Sound Waves ? Energy in sound is extremely small ? Sound energy dissipates to thermal energy while traveling through the air ? Higher frequencies are transformed more rapidly than lower frequencies ? Therefore, low frequencies can travel farther (example: foghorn) Forced Vibrations ? Forced Vibration – the setting up of vibrations in an object by a vibrating force ? Examples: ? ? a tuning fork on a table, will be louder because of the vibration of the table as well as the fork Sounding boards are used in music boxes and stringed instruments to make sound more audible Natural Frequency ? Natural Frequency – a frequency at which an elastic object naturally tends to vibrate if it is disturbed and the disturbing force is removed ? Depends on: ? Elasticity ? Shape of object Resonance ? ? Resonance – the response of a body when a forcing frequency matches its natural frequency Examples: pumping a swing, tuning forks in sympathetic vibrations, marching on bridges Interference in different types of waves ? Interference – a result of superposing different waves, often of the same wavelength. ? Constructive interference results from crest-to-crest reinforcement ? Destructive interference results from crest-totrough cancellation Beats ? ? Beats – a series of alternate reinforcements and cancellations produced by the interference of 2 waves of slightly different frequencies, heard as a throbbing effect in sound waves Examples: tuning instruments, dolphins detecting motion, radar guns detecting speed Example Problem 6 ? What is the wavelength of a 340-Hz tone in air? What is the wavelength of a 34,000-Hz ultrasonic wave in air? ? Answer: ? Wavelength = speed/frequency = 1 m. ? Similarly for a 34,000 hertz wave; wavelength = 0.01 m = 1 cm. Example Problem 7 ? An oceanic depth-sounding vessel surveys the ocean bottom with ultrasonic waves that travel 1530 m/s in seawater. How deep is the water directly below the vessel if the time delay of the echo to the ocean floor and back is 6 s? ? Answer: ? The ocean floor is 4590 meters down. The 6-second time delay means that the sound reached the bottom in 3 seconds. Distance = speed x time = 1530 m/s x 3 s = 4590 m. Example Problem 8 ? You watch a distant person driving nails into a front porch at a regular rate of 1 stroke per second. You hear the sound of the blows exactly synchronized with the blows you see. And then you hear one more blow after you see the hammering stop. How far away is the nail-driving person? ? Answer: ? The woman is about 340 meters away. The clue is the single blow you hear after you see her stop hammering. That blow originated with the next-to-last blow you saw. The very first blow would have appeared as silent, and succeeding blows synchronous with successive strikes. In one second sound travels 340 meters in air. Example Problem 9 ? Two speakers are wired to emit identical sounds in unison. The wavelength in air of the sounds is 6 m. Stat whether the sounds interfere constructively or destructively when you are at a distance of (a) 12 m from both speakers, (b) 9 m from both speakers, and (c) 9 m from one speaker and 12 m from the other. ? Answer: ? (a) Constructively. ? (b) Constructively. (Even though each wave travels 1.5 wavelengths, they travel the same distance and are therefore in phase and interfere constructively.) ? (c) Destructively. The crest of one coincides with the trough of the other. Example Problem 10 ? A grunting porpoise emits sound at 57 Hz. What is the wavelength of this sound in water, where the speed of sound is 1500 m/s? ? Answer: ? Wavelength = speed/frequency = (1,500 m/s)/(57 Hz) = 26 m. ? Alternate method: For sounds of the same frequency in different media, wavelengths are proportional to wave speed. So (wavelength in water)/(wavelength in air) = (speed in water)/(speed in air) = (1,500 m/s)/(340 m/s) = 4.4. Multiply 6 m by 4.4 to get 26 m. Musical Sounds ? While the difference between noise and music is sometimes subjective, the difference can be seen graphically Pitch ? ? Pitch – the “highness” or “lowness” of a tone, as on a musical scale, which is principally governed by frequency Different notes are obtained by changing the frequency of the vibrating sound source by altering: ? Size (wind instruments) ? Tightness (String instruments) ? Mass (xylophone, bells) Sound Intensity & Loudness ? ? ? Intensity – The power per square meter (W/m^2), carried by a sound wave, often measured in decibels Loudness – The physiological sensation directly related to sound intensity or volume ? The ear senses some frequencies better than others, so that a 3500 hz sound at 80 decibels sounds twice as loud as 125 hz at 80 decibels ? Hearing damage begins at 85 decibels and depends on length and frequency ? Damage can be temporary or permanent Decibels: ? Ten decibels is 10x as intense as 0 decibels ? Twenty decibels is 100, or 10^2, times the intensity of 0 decibels ? Thirty decibels is 1000, or 10^3, times the intensity of 0 decibels Quality ? Quality – The characteristic timbre of a musical sound, which is governed by the number and relative intensities of partial tones ? Partial tone – Single-frequency component sound wave of a complex tone. When the frequency of a partial tone,is an integer multiple of the lowest frequency, it is referred to as a harmonic. ? Fundamental frequency – The lowest frequency of vibration, or first harmonic, in a musical tone Musical Instruments ? Grouped into three classes: ? String instruments – low efficiency, resulting in the need for large sections in orchestras ? Wind instruments – sound is made by the vibration of an air column ? Percussion instruments – Vibration of a twodimensional surface ? *Electronic sounds - Some use electrons to produce musical Fourier Analysis ? Fourier Analysis – A mathematical method that disassembles any periodic wave form into a combination of simple sine waves ? Our ear performs a sort of Fourier Analysis automatically Compact Discs ? An analog signal can be changed to a digital signal by measuring the numerical value of its amplitude during each split-second ? ? These values can be expressed in binary CD Players utilize a laser beam on a plastic reflective disk, having pits bout 1/30th the width of a human hair ? The laser reads the pitted surface as zeros or ones (binary) ? DVDs have up to 6X the information of CDs because they have smaller pits Example Problem 1 ? How much more intense than the threshold of hearing is a sound of 10 dB? 30dB? 60 dB? ? Answer: ? The decibel scale is based upon powers of 10. The ear responds to sound intensity in logarithmic fashion. Each time the intensity of sound is made 10 times larger, the intensity level in decibels increases by 10 units. So a sound of ? (a) 10 dB is ten times more intense than the threshold of hearing. ? (b) 30 dB is one thousand times more intense than the threshold of hearing. ? (c) 60 dB is one million times more intense than the threshold of hearing. Example Problem 2 ? A certain note has a frequency of 1000 Hz. What is the frequency of a note one octave above it? Two octaves above it? One octave below it? Two octaves below it? ? Answer: ? One octave above 1000 Hz is 2000 Hz, and two octaves above 1000 Hz is 4000 Hz. One octave below 1000 Hz is 500 Hz, and two octaves below 100 Hz is 250 Hz. Example Problem 3 ? A cello string 0.75 m long has a 220-Hz fundamental frequency. Find the wave speed along the vibrating string. ? Answer: ? The wavelength of the fundamental is twice the length of the string, or 1.5 m. Then the speed of the wave is ? v = f l = 220 Hz x 1.5 m = 330 m/s. (Note that this is for a transverse vibration of the string. A longitudinal sound-wave within the string could have a much greater speed.) Question 1 (3 points) Listen In your own words, explain how different types of instruments are able to produce different notes. Paragraph BI U : > «> E 3 Question 2 (3 points) Listen Which of these is not the same type of wave? Longitudinal waves Shock waves Radio waves Ultrasonic waves Infrasonic waves Question 3 (3 points) Listen What harmonic is this string oscillating in? Amplitude bood standing wave image fourth harmonic third harmonic first harmonic second harmonic Question 4 (3 points) Listen Radio waves travel at the speed of light 300,000,000 m/s. The wavelength of a radio wave received at 89 megahertz ( 1 MHz = 10^6 Hz) is __-_-_ m. (Answer to two decimal places.) Your Answer: Answer Question 5 (3 points) Listen An object that completes 111 vibrations in 7 seconds has a period of seconds. (Answer to two decimal places.) Your Answer: Answer Question 6 (3 points) Listen If you multiple the frequency of a sound 8 times its wavelength is now times what it originally was. (Answer to the second decimal place.) Your Answer: Answer Question 7 (3 points) Listen When the air closest to the ground is colder than air that is above it sound waves tend to be refracted downward sound waves travel without refraction. sound waves tend to be refracted upward. Question 8 (3 points) Listen The fisherman notices wave crests passing his anchor chain every 3 seconds. He estimates the speed of the waves to be 3 m/s. Calculate the wavelength of the waves. The wavelength is m. (Answer to the second decimal place.) Your Answer: Answer Question 9 (3 points) Listen In your own words, explain why sound travels at different speeds in different media and why some are faster and some are slower. Paragraph BIU ... Question 10 (3 points) Listen A wave travels an average distance of 7 meters in 4 second(s). The wave's velocity is m/s. (Answer to two decimal places.) Your Answer: Answer Question 11 (3 points) Listen A tuning fork with a frequency of 106 Hz is sounded at the same time second tuning fork is struck. You hear 4 beats per second. If you know that the second tuning fork has a higher frequency than the first tuning fork, calculate its frequency. The frequency of the second tuning fork is ____ Hz. (Answer to the second decimal place.) Your Answer: Answer Question 12 (2 points) Listen Compared to a flute the wavelengths the sounds of a foghorn are the same shorter longer Question 13 (3 points) Listen Refraction of sound can occur in Neither air nor water Air. Water. Both air and water. Question 14 (3 points) Listen A 35 vibration per second wave travels 40 meters in 1 second(s). The wave speed is m/s. (Answer to two decimal places.) Your Answer: Answer Question 15 (3 points) Listen In your own words explain the difference between harmonics and octaves of the note "G3" (frequency = 196 Hz). What would be the harmonics and octaves of this note? Are they the same? Paragraph BI U . EQ Ch Question 16 (3 points) Listen Which is fastest? sound in copper sound in a vacuum sound in air sound in oil Question 17 (3 points) Listen A fishing-boat captain says. "It is rough out there - the waves are 4 meters high." He probably means that the amplitude of the wave is --- m. (Answer to two decimal places.) Your Answer: Answer Question 18 (3 points) Listen An aircraft that flies faster than the speed of sound is said to be Supersonic. Impossible. Subsonic. Question 19 (3 points) Listen As we become older, the frequency range of human hearing remains relatively constant. the frequency range of human hearing increases. the frequency range of human hearing decreases. Question 20 (3 points) Listen Radio waves travel at the speed of light 300,000,000 m/s. What is the wavelength of radio waves that are received at 95.0 MHz on your FM radio dial? 1 MHz = 10^6 Hz. The wavelength is _______ m. (Answer to the second decimal place.) Your Answer: Answer Question 21 (3 points) Listen When designing a music hall acoustical engineer is most concerned about beats. acoustical engineer is most concerned about wave interference. acoustical engineer is most concerned about modulation. acoustical engineer is most concerned about forced vibrations. acoustical engineer is most concerned about resonance. Question 22 (3 points) Listen If the period of a wave is 1.6 seconds, calculate the frequency. The frequency is --- Hz. (Answer to the second decimal place.) Your Answer: Answer Question 23 (3 points) Listen The frequency of the minute hand on a clock is 1/3600 Hz O 1/60 Hz O 1 Hz 60 Hz 3600 Hz Question 24 (3 points) Listen Sound will be louder if a struck tuning fork is held with its base against a table top a struck tuning fork is held with its prongs in shallow water. a struck tuning fork is held in your closed fist. O a struck tuning fork is held in the air. Question 25 (3 points) Listen How many anti-nodes are present in this image? Amplitude bood two four five three Question 26 (3 points) Listen On a standing wave, an antinode is a position of Minimum amplitude. Maximum amplitude. O Half amplitude Question 27 (3 points) Listen A standing wave occurs when The speed of the wave is zero and near zero. Two waves overlap The amplitude of a wave exceeds its wavelength. A wave reflects upon itself. Question 28 (3 points) Listen A wave oscillates up and down 3 complete cycles each second. If the wave travels an average distance of 8 meters in one second, calculate its wavelength. The wavelength is -----m. (Answer to two decimal places.) Your Answer: Answer Question 29 (3 points) Listen The natural frequency is highest for Small bell O Large bell. Medium size bell. Question 30 (14 points) Listen There are two diagrams below of the same wave. One is in respect to time and the other is in respect to distance. This problem is worth 14 points and has 7 parts please be sure to type out your answers to each - do not forget to number your answers and include units. 1) Give the value of the period (include units) 2) Give the value of the wavelength (include units) 3) Give the value of the amplitude (include units) 4) Find the frequency (include units and show your work) 5) Find the velocity (include units and show your work) 6) If you were to draw a wave that COMPLETELY CANCELS the wave in the first diagram - how would you draw it on the graph? Please describe it's appearance including information about it's amplitude, wavelength, and locations of it's maximum(s), and minimum(s), and where it would intersect the x-axis (where it has "0" amplitude) 7) If you were to draw a wave that is COMPLETELY CONSTRUCTIVE to the wave in the first diagram - how would you draw it on the graph? Please describe it's appearance including information about it's amplitude, wavelength, and locations of it's maximum(s), and minimum(s), and where it would intersect the x-axis (where it has "0" amplitude) 25 20 15 10 displacement (cm) has "0" amplitude). 25 20 15 10 displacement (cm) O -10 -15 20 -25 0 10 20 30 40 50 time (sec) 25 20 15 10 displacement (cm) 0 -6 10 20 -25 70 80 90 100 110 120 130 140 150 distance (meters) A Paragraph BIU