Chapters 19 & 20 Notes: Oscillations, Waves, and Sound

Pendulums and Simple Harmonic Motion

• A pendulum consists of a mass at the end of a string that oscillates back and forth.
• The time it takes for the pendulum to complete one full oscillation (back and forth) is fixed and depends primarily on the length of the string.
• As long as the amplitude (the extent of the swing) isn't too large, the time for each oscillation remains the same.
• This repeating motion is called simple harmonic motion. The main factor affecting a pendulum's motion is its length.
• Frequency is how many oscillations occur in a certain amount of time.
  • Units: oscillations per second, also known as Hertz (Hz).
  • kHz in AM radio, MHz in FM radio.
• The period ($T$) is the time for one oscillation.
  • $T = 1 / frequency$
  • A large frequency implies a small period, and vice versa.
• Amplitude is the maximum displacement from the center.
• Many objects exhibit this type of periodic motion, following Hooke's Law.

Hooke's Law and Restoring Force

• Hooke's Law: Restoring force is proportional to the displacement.
• Force is proportional to the change in position (displacement).
• At the center, there's no displacement.
• The farther you are from the center, the greater the force pulling back towards the center.
• Because of the interaction between force and displacement, the time for each oscillation remains constant regardless of amplitude.
• The pendulum’s motion slightly depends on the angle, but as long as the angle (and amplitude) is small, it follows Hooke's Law.
• Displacement is how far an object is from the center.
• For Hooke's Law to apply, if displaced one way, the force acts in the opposite direction, pulling it back towards the center.
• If supporting the object at the top it swings back and forth, thus periodic motion. Supporting it at the bottom it goes faster.

Waves and Their Properties

• Waves extend through space.
• Waves involve the motion of two things:
  • The wave itself.
  • The material that makes up the wave.
• Two main classifications of waves:
  • Transverse waves
    • The wave and the medium move at right angles.
    • Example: A sports wave in a stadium. The wave moves around the stadium, but the fans move up and down.
  • Longitudinal waves
    • The wave and the medium move in the same direction.
    • Example: Traffic jam. Cars back up at a red light, and the wave of stopping propagates backward as cars move forward.

Frequency, Wavelength, and Wave Speed

• Waves have frequency and wavelength.
• Wavelength: The distance that the wave travels in one oscillation.
• Wave speed ($v$) can be calculated using wavelength ($\lambda$) and period ($T$) or frequency ($f$).
  • $v = \lambda / T$ or $v = \lambda * f$

Doppler Effect

• Imagine a bug moving across water, creating ripples.
• If the bug is moving, the center of the circles will be shifted. The waves will be closer together in the direction of motion and further apart in the opposite direction.
• This results in a higher frequency in the direction of motion and a lower frequency in the opposite direction.
• Doppler Effect: The change in frequency with motion.
• The waves will get closer together in the direction that the object is moving and further apart in the opposite direction. Because waves are closer in the direction that the bug is moving you have a higher frequency in that direction and lower frequency in the opposite direction.
• If the bug travels at the speed of the wave propagation, all the waves will be on top of each other.
• If an object is moving at the speed of sound, you get a shockwave.

Shockwaves

• A plane traveling faster than the speed of sound produces a shockwave.
• Similarly, a boat traveling fast enough produces a wake.
• If the object producing the wave is traveling faster than the wave speed, a bow wave (wake of a boat) or shockwave (plane) is produced.
• The crack of a whip is the end of the whip traveling faster than the speed of sound, dissipating energy as sound.

Sound Waves

• Chapter 20 focuses on sound waves.
• Sound usually involves vibrating air but can travel through any medium by changing pressure.
• Sound requires a medium to travel through.
• The material undergoes compression (increase in pressure) and rarefaction (decrease in pressure).
• Without material, sound cannot be transmitted (no sound in space).

Audible and Inaudible Sound

• Audible sound: Sound we can hear (20 Hz - 20,000 Hz).
• This range decreases with age.
• Infrasonic: Frequencies below 20 Hz (inaudible).
• Ultrasonic: Frequencies above 20,000 Hz (inaudible).

Pitch and Echoes

• Pitch: Our brain's interpretation of sound frequency.
• High frequency = high pitch.
• Echoes: Reflections of sound.
• Reverberation: Multiple reflections of sound from multiple surfaces.
• Echo: Reflection of sound off a surface where the incoming angle is the same as the outgoing angle.

Refraction of Sound

• Refraction: Bending of sound waves at a surface.
• Occurs when a wave changes speed going from one material to another.
• This can happen due to different materials or temperature gradients.
• Angles are measured from the normal (perpendicular) to the surface.
• Reflection: Incoming angle = outgoing angle.
• Refraction angle depends on the speeds.
• Fast material to slower material = angle decreases.

Ultrasonic Imaging

• Uses reflections and refractions of sound to reconstruct what's happening inside the body.
• Less invasive than surgery.
• Ultrasonic uses high frequency.
• Speed of sound within the body is roughly constant.
• Higher frequency = shorter wavelength.
• Small wavelength = can see smaller details.
• Ultrasonic is used to avoid damaging ears.

Interference

• Interference: Two or more waves overlapping or interacting.
  • Constructive Interference: Waves are up at the same time and down at the same time and add together, resulting in a single, larger wave (larger amplitude).
    • Waves are in phase.
  • Destructive Interference: Waves are opposite each other causing them to cancel out.

Noise Canceling and Standing Waves

• Noise-canceling headphones use destructive interference to cancel out external sounds.
• Standing waves occur when a wave interferes with itself, usually due to reflection.
• Limited number of waves will constructively interfere on a string of a particular length.
• Always end up with some multiple of half wavelengths.

Harmonics

• First harmonic:
  • Most of the energy.
  • One frequency.
• Second harmonic:
  • Twice the frequency of the first harmonic.
• Third harmonic:
  • Three times the frequency of the first harmonic.
• Fourth harmonic:
  • Four times the frequency of the first harmonic.
• Different instruments sound different because of the different ratios of harmonics they produce.
• A piano and a trumpet playing the same note sound different because they have different ratios of harmonics.
• One instrument might have all of its energy in the first harmonic while another has lots of energy in the even or odd harmonics.

String and Wind Instruments

• String instruments:
  • Drawn, this is for a string we have string instruments, there are also wind instruments. You end up with roughly the same pattern. Just rather than on a string, it's a pressure difference within the air column for a wind instrument.
  • Usually something producing oscillations, and the instrument amplifies particular frequencies.
  • Striking strings or valves on a trumpet affect which frequencies constructively interfere.
  • Sounding Board: Most string instruments have a sounding board. The body of the guitar acts as a sounding board.
    • Guitar strings alone are not loud; the body of the guitar vibrates, moving more air so you are ablt to hear the sound.
    • Sounding board transfers energy to the air more quickly. Energy is dissipated more quickly.

Resonance Frequencies

• The body of a guitar acts as a sounding board, not very loud without a body on it.
• A harp string oscillates for a longer time because it has no sounding board.
• The frequency of the object matches the frequency of the other objects.
• Resonance: The frequency of the source of the sound and the frequency of the object match.
  • If someone sings at the exact frequency, the energy will build up within the crystal and you could hypothetically shatter the glass if you increase the amplitude enough that it breaks the object.
  • You have to be careful with resonance frequencies.
• Bridges can collapse because resonance frequency matched some other frequency in the surroundings.
  • Lumineros Bridge due to wind. The wind that passed over the bridge would cause the bridge itself to oscillate and eventually ripped itself apart.
  • If you are swinging on as swing set you have to time the motion of your legs so you are increasing the rate of the oscillation.

Beat Patterns

• Beat Pattern: Two waves of similar frequency.
  • If they were exactly the same frequency you'd either get constructive or destructive interference but if they are just similiar in frequency then they will alternate between the two. All points they'll be in phase and then at other points they will be out of phase as the waves line up.
  • How quickly depends on the difference between the waves.
  • You can use this relationship to tune an instrument.
  • Have a tuning fork and it's exactly the right pitch, then you can play your instrument.
  • If they were in tune you just hear a steady note, but if they're out of tune, depending on how far they're out of tune affects how quickly it alternates between the constructive and destructive.

Practice Test Questions

• Largest momentum relative to the Earth: A speeding train (momentum = mass x velocity).
• Difference between impulse and impact force: Impulse is force multiplied by time.
• Tiny gun firing a bullet more massive than gun: Target would be safer than shooter. The bullet fires and the gun moves back towards you much faster and the shooter would be in danger.
• Two elders with same size and shape, heavier one has greater: Momentum. They have the same but the acceleration on the heavier one the momentum would be different.
• Bending knees when jumping from elevated position: Makes time of impact greater. Makes the average force your body experiences. If there is ten times the time then there's one tenth the force.
• Force on apple hitting the ground depends upon: All of these.
  • Depends on the time of the impact, also depends on the speed just before it hits, but also depends on whether it's bouncing or not.
• One kilogram choke of putty collides with and sticks to a five kilogram bowling ball initially at rest. Momentum of bowling ball? So if you are looking at the momentum it's going to be the same. Momentum before and after will be the same.
  • Before you have the momentum the putty. But the momentum of ball is five times zero. Because starting at rest the ball doesn't have any momentum. The total is going to be the same before and after. One times one plus five times zero which is going to be that one kilogram meter per second.

Cannon and Rocket Questions

• Rocket accelerates because of: the exhaust gases. Ball with long barrel increases: muzzle velocity.
• Shark speed: 5kg shark swims at 1 m/s. 1kg fish attempts to swim away toward the shark w/velocity of 4m/s, velocity of shark immediately after capturing lunch?
  • Before the meal you have a mass of 5 with velocity of 1. For the fish you have a mass of 1 that is -4.
  • So then is 5-4 which is 1 before the collision. After the collision you got a total mass a 6, total momentum divided by the total mass. One over six. So one over six meters per second

Car Collisions and Stationary Walls

• 5000 kg freight car runs into a 10000 kg freight car that starts at rest.
  • 5000 times its initial, plus the 10,000 times zero. If both are moving with velocity of 2 m/s then what would this be?
  • After the collision, both of them are moving, so 15,000 both are moving at two mss, then give us 30,000.
  • 5,000 *initial velocity + 10,000 *0 *initial velocity=0, so then we get 6, so just do the 30,000 / 5,000=6.
• Pushing against a stationary wall for half an hour or a whole hour. Looking for distance, the distance is zero. So regardless of how long.

Energy and Power Questions

• Is twixe much work to perform but you have twice as much time? Work divided by time is the same amount of power. You had twice as much work, but twice as much time. Twice the denominator, still the same amount of power.
• Doubling something increases the height: energy is mass times gravity times height.
  • If we double the height, will double the energy. Exponent object may have. Potential energy depends on location, location.

Airplane Momentum, Potential Energy Machines and Rolling

• Bullets from a plane in the forward direciton. Is decreased. It's taking momentum away from the plane.
  • A-ten Warthog: Firing forward it is taking momentum away with the plane.
• Does a hydraulic press increase Energy? No, create: perpetual energy machine.
  • Hydraulic press? Inclined plane? Increase force, not energy.
• Kinetic energy: half way =same. Potential to kinetic energy. Have equal amounts.

Bowling Balls, Cars, and Jacks

• No work is done by gravity on ball. Because force runs up and down. The forces will be up and down. Zero force to side. Not C. Is similar to C
• Car four times faster. Equation? Energy gives us for squarred. Four times as fast means fou times the speed that doesn't mean four times the energy, that makes 16 times the energy
• Jacl system increases load. What's efficiency = 50 percent.

Fast Cars and Objects with Kinetic Energy

• Without 4 times as much energy you are going to skid four times as far. Object Kinetic energy. Must have = momentum.

Bullet and Rifle Momentum, Merry-Go-Rounds and Wheel Diameters

• Equal = kinetic energy. It's bullet. So the bullet and riffel momentum. If we think about the bullet and the riffs so the rifle that bullet has more last the bullet is going to have a higher speed greater speed. A and B. If we think about our kinetic energy. Easier to think about the other equation.
• Those a merry go round greatest speed = farthest points
• Tire with diameter will read. Less Because speedometer isn't measuring the distance. You are increasing will hav eless rotation for the same distance Velocity = angular . Because if the is slower can accidentally.

Coins/Rings and Gravitational Collapse

• Coin rolls, then is less inertia to roll. Ice skater brings arms in
• Center gravity. What to bring forward. One of you will go higher.
  Gravitatinal collapse rate is spinning, it goes faster.

Waves, Pendulums, and Oscillation Frequencies

• Traverse =right angle. Lenght/gravity. Pendulum planet move. Or levitate.
• Hundred Vibration/find cycle.
• 1/10 will give a period per time.

Wave Barriers and Speed Questions

• Wave Barrier= same speed. Wave=2.20 ms. Red is moving away. Most red shift. That are other= reduce amp/sound

Sound, Temperatures and Steel

• Best is. Hear = the middle range. 41 =steel. A sound if the is =warmer. So also temp is air. Speed is diff mass and velocity.

Sound Bending, Bas fiddles, and Inhaling Helium

• Changes shape + the reason. High pitch =faster.