4.1: Mechanical Waves Written Response #1
1. What is energy? 2. What is mechanical energy? 3. True or False: displacement in opposite directions add together. 4. How is speed calculated? What are the units? 5. What are the standard units (SI) of distance? Time? 6. What happens to the spacing of particles within a solid or liquid as the temperature increases? 7. What happens to the speed of the particles in a solid, liquid, or gas as the temperature is increased? Written Response #1 - Answers
1. What is energy? 5. What are the standard units • Ability to do work (SI) of distance? Time? 2. What is mechanical energy? • Meter; second • Energy due to the motion of 6. What happens to the position of an object; ME = KE spacing of particles within a + PE solid or liquid as the 3. True or False: displacement temperature increases? in opposite directions add • The particles move farther together. apart • False; the displacement 7. What happens to the speed subtracts of the particles in a solid, 4. How is speed calculated? liquid, or gas as the What are the units? temperature is increased? • Speed = distance / time; • The particles move faster meters per second (m/s) Introduction to Waves Mechanical Waves
• Types of Mechanical Waves: • sound waves, visible light waves, radio waves, microwaves, water waves, sine waves, telephone chord waves, stadium waves, earthquake waves, waves on a string, slinky waves What is a Wave?
• Wave: rhythmic disturbances that carry energy through matter or space • Medium: material through which a wave transfers energy • Solid, liquid, gas, or combination • Example: water is a medium for waves. • Electromagnetic waves don’t need a medium (example: visible light) Mechanical Waves
• A mechanical wave is created when a source of energy causes a vibration to travel through a medium. • Vibration: a repeating back-and-forth motion Mechanical Waves
• Let’s use a slinky wave as an example. • When the slinky is stretched from end to end and is held at rest, it assumes a natural position known as the equilibrium or rest position. • To introduce a wave here we must first create a disturbance. • We must move a particle away from its rest position. Mechanical Waves
• One way to do this is to jerk the slinky forward • the beginning of the slinky moves away from its equilibrium position and then back. • the disturbance continues down the slinky. • this disturbance that moves down the slinky is called a pulse. • if we keep “pulsing” the slinky back and forth, we could get a repeating disturbance. Mechanical Waves
• This disturbance would look something like this:
• This type of wave is called a longitudinal wave. • The pulse is transferred through the medium of the slinky, but the slinky itself does not actually move. • It just displaces from its rest position and then returns to it. • So what really is being transferred? What is Transferred in Mechanical Waves? • Energy is being transferred. • The metal of the slinky is the medium in that transfers the energy pulse of the wave. • The medium ends up in the same place as it started…it just gets disturbed and then returns to it rest position. Types of Mechanical Waves
• Mechanical waves are classified by the way they move through a medium. • The three main types of mechanical waves are • Transverse waves • Longitudinal waves • Surface waves Examples of Longitudinal and Transverse Waves: • Longitudinal • Transverse Transverse Waves
• Transverse Waves: a wave that causes the medium to vibrate at right angles to the direction in which the wave travels • medium moves perpendicular to the direction of wave motion Transverse Waves: Need to Know
• Crest: the highest point of the wave above the rest position • Trough: the lowest point below the rest position • Crests and troughs are not fixed points • Node: a point on a standing wave that has no displacement from the rest position • Wavelength: the distance between a point on a wave and the same point on the next cycle of the wave • Amplitude: the maximum displacement of a medium from the rest position Mechanical Waves
• Draw the wave below in your notebook • In our wave here the dashed line represents the equilibrium position. • Once the medium is disturbed, it moves away from this position and then returns to it Mechanical Waves
• The points A and F are called the crests of the wave. • This is the point where the wave exhibits the maximum amount of positive or upwards displacement
crest Mechanical Waves
• The points D and I are called the troughs of the wave. • These are the points where the wave exhibits its maximum negative or downward displacement.
trough Mechanical Waves
• The distance between the dashed line and point A is called the amplitude of the wave. • This is the maximum displacement that the wave moves away from its equilibrium.
Amplitude Mechanical Waves
• The distance between two consecutive similar points (in this case two crests) is called the wavelength. • This is the length of the wave pulse
wavelength Wave Anatomy – Transverse Waves
corresponds to wavelengthcrests the amount of energy carried by the wave amplitude
amplitude nodes
wavelength troughs Transverse Waves Longitudinal Waves
• Longitudinal waves: a wave in which the vibration of the medium is parallel to the direction the wave travels (back and forth) • Compression: an area where the particles in a medium are spaced close together • Rarefaction: an area where the particles in a medium are spread out • Also referred to as “compressional waves” Wave Anatomy – Longitudinal Waves
compression wavelength
rarefaction wavelength
Amount of compression corresponds to amount of energy AMPLITUDE. Longitudinal Waves Surface Waves
• Surface waves: a wave that travels along a surface separating two mediums • Motion is up and down; is perpendicular to the direction in which the wave travels • Motion is also back and forth; parallel to the direction in which the wave travels • Added together=circular motion • Most waves do not transport matter from place to place. (Exception: ocean waves) Surface Waves Labeling Waves - Handout 4.2: Properties of Waves Properties of Mechanical Waves
• Properties used to describe waves are: • Period • Frequency • Wavelength • Speed / Velocity • Amplitude. Frequency and Period
• Periodic motion: any motion that repeats at regular time intervals • Period: the time required for one cycle, a complete motion that returns to its starting point • Frequency: the number of complete cycles in a given time (cycles/second or hertz) • A wave’s frequency equals the frequency of the vibrating source producing the wave. Properties of Mechanical Waves: Frequency • Frequency ( f ) • Number of waves passing a point in 1 second • Hertz (Hz) (1 Hz = 1 cycle / second)
• Shorter wavelength → higher frequency → higher energy Period and Frequency – Handout (19.1) Wavelength
• Wavelength: the distance between a point on one wave and the same point on the next cycle of the wave • Increasing the frequency of a wave decreases its wavelength • Transverse Waves: between adjacent crests or adjacent troughs • Longitudinal Waves: between adjacent compressions or rarefactions Frequency and Wavelength of Transverse Waves
Frequency Wavelength Amplitude
• Amplitude: the maximum displacement of the medium from its rest position • It takes more energy to produce a wave with higher crests and deeper troughs. • The more energy a wave has, the greater is its amplitude. Wave Speed
• Wave Speed = Wavelength (m) x Frequency (Hz) • Units: m/s • Wave speed can change if: • Enters a new medium • Pressure changes • If you assume that waves are traveling at a constant speed, then wavelength is inversely proportional to frequency. Wave Velocity
• Velocity ( v ) • v = × f • Speed of a wave as it moves forward • Depends on wave type • v: velocity (m/s) and medium • : wavelength (m) • f: frequency (Hz) Written Response #2
• Find the velocity of a • Given: wave in a wave pool if • v = ? its wavelength is 3.2 m • = 3.2 m and its frequency is • f = 0.60 Hz 0.60 Hz. • Work: • v = x f • v = (3.2 m)(0.60 Hz) • v = 1.92 m/s Written Response #3
• One end of a rope is • Given: vibrated to produce a • v = ? wave with a wavelength • = 0.25 m of 0.25 m. The • f = 3.0 Hz frequency of the wave • Work: is 3.0 hertz. What is the • v = x f speed of the wave? • v = (0.25 m)(3.0 Hz) • v = 0.75 m/s Written Response #4
• An earthquake • Given: produces a wave that • = 417 m has a wavelength of • v = 5,000 m/s 417 m and travels at • f = ? 5,000 m/s. What is its • Work frequency? • f = v ÷ • f = (5,000 m/s) ÷ (417 m) • f = 12 Hz Written Response #5
• A motorboat is tied to a • Given: dock with its motor • v = ? running. The spinning • = 0.1 m propeller makes a • f = 4.0 Hz surface wave in the • Work: water with a frequency • v = x f of 4 Hz and a • v = (0.1 m)(4.0 Hz) wavelength of 0.1 m. • v = 0.4 m/s What is the speed of the wave? Written Response #6
• What is the wavelength • Given: of an earthquake wave • = ? if it has a speed of • v = 5,000 m/s 5,000 m/s and a • f = 10 Hz frequency of 10 Hz? • Work: • = v ÷ f • = (5000 m/s) ÷ (10 s) • = 500 m Written Response #7
• A wave on a rope has a • Given: frequency of 3.3 Hz and • v = ? a wavelength of 1.2 m. • = 1.2 m What is the speed of • f = 3.3 Hz the wave? • Work: • v = x f • v = (1.2 m)(3.3 Hz) • v = 3.96 m/s 4.2: Wave Worksheet - Handout Wavelength – Handout (20.1) Lab: Waves in a Slinky 4.3: Behavior of Waves 4.3: Wave Characteristics Review - Handout Behavior of Waves
• Many interactions can occur as waves move back and forth: • Reflection • Refraction • Diffraction • Interference Wave Behavior: Reflection
• Reflection: what occurs when a wave bounces off a surface that it cannot pass through • Example: a ball thrown at a wall (bounces back) • Reflection does not change the speed or frequency of a wave, but the wave can be flipped upside down. Wave Behavior: Refraction
• Refraction: the bending of a wave as it enters a new medium at an angle. • When a wave enters a medium at an angle, refraction occurs because one side of the wave moves more slowly than the other side. • Refraction of a wave occurs only when the two sides of a wave travel at different speed. Behavior of Waves: Refraction
• Wave bends • Velocity decreases • Wavelength decreases Behavior of Waves: Diffraction
• Diffraction: the bending of a wave as it moves around an obstacle or passes through a narrow opening. • A wave diffracts more if its wavelength is large compared to the size of an opening or obstacle. Behavior of Waves: Diffraction
• Written Response #8: why do you hear someone talking outside of a room when you do not see him or her? Behavior of Waves: Interference
• Interference: what occurs when two or more waves overlap and combine together or when two waves meet while traveling along the same medium. • Waves can occupy the same region of space and continue on. • Two types of interference: • Constructive interference • Destructive interference. Behavior of Waves: Interference
• Constructive Interference: what occurs when two or more waves combine to produce a wave with a larger displacement. • The amplitudes of two waves can add together for a greater total amplitude. Behavior of Waves: Interference
• Destructive Interference: what occurs when two or more waves combine to produce a wave with a smaller displacement • Can reduce the amplitude of a wave • Example: two waves moving towards each other, one having a positive (upward) and one a negative (downward) amplitude. Behavior of Waves: Interference Behavior of Waves: Standing Waves • Standing Waves: a wave that appears to stay in one place (it does not seem to move through a medium) • Node: a point on a standing wave that has no displacement from the rest position • At nodes there is complete destructive interference between incoming and reflected waves • Antinode: a point where a crest or trough occurs midway between two nodes. • Why does a standing wave happen only at particular frequencies? • A standing wave forms only if half a wavelength or a multiple of half a wavelength fits exactly into the length of a vibrating cord Standing Waves (20.1) 4.3: Wave Interactions - Handout Wave Interactions Lab 4.4: Sound and Hearing Written Response #9: Draw the wave to the right, label the correct places and define the terms. Introduction to Sound
• Oscilloscope Sound and Hearing
• The Doppler Effect: a change in sound frequency caused by motion of the sound source (siren), motion of the listener, or both. • As a source of sound approaches, an observer hears a higher frequency. • As a source of sound source moves away, the observer hears a lower frequency. Doppler Effect
Stationary source Moving source Supersonic source
waves combine to same frequency in lower higher produce a shock wave all directions frequency frequency called a sonic boom Written Response #10 - Doppler Ball Demonstration 1. Describe the sound coming from the ball when the ball is stationary. 2. Describe the sound coming from the ball when the ball is moving toward you. 3. Describe the sound coming from the ball when the ball is moving away from you. 4. Describe the sound coming from the ball when you walk towards and away from the ball. Applications of the Doppler Effect
• Applications • Radar • Weather • Astronomy • Medical instruments The Doppler Effect Speed of Sound
• 344 m/s in air at 20°C • Depends on: • Type of medium • travels better through liquids and solids • can’t travel through a vacuum • Temperature of medium • travels faster at higher temps Speed of Sound Calculations - Handout 1. Sound is collected by ear the and directed into the ear canal. 2. Sound waves travel through the ear canal and strikes the eardrum. Human Hearing 3. The eardrum is also called the tympanic membrane and vibrates when sound strikes it. 4. The vibrations in the ear drum make the bones of the middle ear vibrate as well and they pass the vibrations through the middle ear. 5. When the small bones of the middle ear vibrate they push on a small window in the cochlea which causes the fluid inside it to vibrate as well. 6. Inside the cochlea there are tiny hair cells that are moved around by the fluid after the tiny bones in the ear vibrate. 7. The tiny hair cells in the ear are attached to nerves and send signals to the brain through the auditory nerve about the sound they heard. Written Response #11
• Sometimes hearing damage is caused by sounds that are too loud, or have too much amplitude. This can cause damage to two different parts of the ear because the vibrations (sound waves) are too big. Looking at this diagram, discuss the two different parts of the ear that can be damaged due to sounds that are too loud. Human Hearing: Pitch
• Pitch • highness or lowness of a sound ultrasonic waves • depends on frequency of sound wave • human range: 20 - 20,000 Hz Human Hearing: Intensity
• Intensity • volume of sound • depends on energy (amplitude) of sound wave • measured in decibels (dB) Human Hearing
DECIBEL SCALE
120 110 100 80 70
40
18 10 0 Decibel Scale - Handout Seeing with Sound – Ultrasonic waves (above 20,000 Hz) SONAR: “Sound Navigation Medical Imaging Ranging” Wave Puzzle and Practice Problems - Handout