Physics - Waves and Oscillations

Main ideas and key takeaways from oscillations, waves, and sound units

The force can be derived as the negative _____ of the potential function

Negative gradient

When a potential energy slope is negative - force is ____

positive

When potential energy slope is positive - force is _____

negative

When an object is at the top of the hill (local max), it is in _____ equilibrium, and what happens if you displace this object?

Unstable equilibrium - when you displace the object, it will not return there

when object is in bottom of valley (local min), it is _____ equilibrium, and what happens when you displace the object?

Stable equilibrium - when you displace object, it will oscillate around this point

For a potential energy function - what happens in a flat area?

It is neutral - the object will not move when you push it

Turning points occur where all the energy in the system is ______ and velocity is _____, and direction of motion ______

Potential energy, velocity is zero, and direction reverses

what is the definition of simple harmonic motion?

When oscillation repeats itself over same path, motion is periodic

in SHM, why does the object move back and forth?

There is a restoring force directed at the equilibrium

Period and frequency are the ____ of each other

Inverse

Define period and frequency

Period is time it takes for 1 complete cycle, frequency is number of cycles that occur per unit time

For a spring - the greater the mass, the _____ the frequency, and why

Lower frequency - the higher inertia leads to lower response time

A stiffer spring (higher k) leads to a ____ frequency - why?

higher frequency, the large k means a greater restoring force and quicker response time

A wave that repeats quickly has _____ frequency and ____ period

high frequency and short period

A wave that repeats slowly has ____ frequency and _____ period

low frequency and long period

For oscillations, what does velocity tell you?

How fact and in what direction the object is moving - refers to the position of the object itself

For oscillations - what does acceleration tell you?

How quickly the object’s velocity is changing - refers to the position of the object itself

for oscillations - velocity is _____ (max/min) at the equilibrium

Max at the equilibrium

For oscillations - velocity is zero at the _____ positions, where direction ____

extreme positions where direction reverses

For oscillations - Acceleration is always directed towards _____ position, meaning it is opposite to ____

equilibrium position, displacement

For oscillations - acceleration is max at ____, zero at ____

max at extreme positions, zero and the equilibrium

displacement, velocity, and acceleration are all ____, but out of phase

sinusoidal

Velocity is ___ degrees out of phase with displacement, acceleration is ____ degrees out of phase with displacement

90, 180

Hooke’s law - force exerted by spring is _____ proportional (by K) to the ___ from equilibrium

negatively proportional, distance from equilibrium

why is hooke’s law negatively proportional?

negative because the force acts opposite to the displacement - restoring force

where is the equilibrium position on the spring?

every spring has a natural length at which net force on the mass is zero

Kinetic energy for SHM is max at ____, and zero at the _____

max at equilibrium, zero at the extremes

Total energy of system for SHM is dependent on _____ and _____

amplitude and spring constant

A pendulum only undergoes SHM for _____

small angles - usually less than 15 degrees

What provides the restoring force that pulls the ball back towards equilibrium

Gravity does

For a simple pendulum - period is independent of ____ and ___, but depends on _____ and ____

independent of mass and amplitude, depends on length and gravity

Mechanical waves must travel through a ____, and always travel away from _____

through a medium, away from the source

what happens to each particle in mechanical waves?

the wave itself moves with a velocity, but each particle merely oscillates around an equilibrium point

waves carry ______ from one place to another, but do not transfer _____ over long distances

energy, matter

Transverse vs longitudinal

Transverse - medium oscillates perpendicular to direction of propagation of wave
Longitudinal - vibration of particles is along same direction as wave motion

Amplitude is ___

max displacement of particles from equilbrium and height of the crest/depth of the trough

wavelength is ____

distance between two crests

what does wave velocity measure?

Measures the speed at which the wave propagates through the medium - how fast energy is moving through

For a transverse wave - greater tension will lead to ___ velocity because ____

velocity will be higher because each segment of the cord is in tighter contact with its neighbors - and higher restoring force for each particle

For a transverse wave - higher linear density means _____

Lower velocity

for longitudinal wave - wave velocity increases with _____ elastic force factor and decreases with _____ inertia factor

Higher, higher

As waves travel through a medium, the energy is transferred to vibrational energy from ____ to ____

particle to particle

Larger amplitude and larger frequency more ____

more energy

Power is the _____, and quantifies how ____ the wave delivers energy

average rate of energy transferred - how quickly it delivers energy

Intensity is the _____ transferred across unit area ____ to energy flow

average power, perpendicular

Intensity describes how _____ the energy transfer is, when you spread it over large distances, the intensity _____

concentrated - the energy decreases

Reflection occurs when a wave encounters a boundary/obstacle and _____ back into original medium - the wave changes ____ but continues ____

bounces back, changes direction, continues oscillating

Transmission happens when a wave _____

passes from 1 medium into another

When transmission happens, the wave continues propagating but with changes to _____

speed, wavelength, direction

For transmission, what remains the same across boundaries?

the frequency

Constructive versus destructive interference

Constructive - waves are exactly in phase and add up
Destructive - waves are out of phase by 180 or half a wavelength, cancel out

Standing waves are formed by the superposition of two waves of ____ frequency and amplitude traveling in _____ direction

Same frequency and traveling in opposite directions

Standing waves do not transfer ____, but instead _____ in time while spatial form is ____

do not transfer energy, oscillates in time, spatial form is fixed

Nodes vs anti nodes

Nodes - Points that remain fixed - zero displacement due to destructive interference
Anti nodes - points where amplitude reaches max due to constructive interference

For standing waves - what is distance between two adjacent nodes

half a wavelength

what is the law of reflection?

reflected rays bounce off at same angle as incident angle

what is refraction?

the bending of a wave as it passes from one medium to another

Refraction - change in direction occurs because wave changes ___ when it moves between different ____
Why does this bend the wave?

speeds, medium
part of the wavefront entering the new medium slows down or speeds up, causing wave to bend

what does snell’s law relae?

Relates angles of incidence and refraction, and refractive indexes

what is the source of a sound

a vibrating object

what does the speed of sound depend on?

the medium in which it travels - the temperature, the density, the elasticity

Lower pitch = ____ frequency, higher pitch = ____

lower, higher

Intensity of sound uses decibel system which is log based - to produce sound twice as loud, you need___ the intensity

10x the intensity

Sound intensity decreases in line with ______

inverse square law

Loudness is related to __

energy in the sound wave

What happens with constructive and destructive interference for sound waves?

constructive - person will hear a louder sound
destructive - sound will completely cancel out

Beats - two sound waves with slightly different ____ interfere with each other

frequencies

Beats have a periodic fluctuation in the ____, producing a rhythmic wobbling or pulsing effect

loudness or intensity

For beats, the perceived pitch of the resulting sound is the ____

average of the two frequencies

If sound is moving away from you - pitch will seem ___

lower

if sound is moving towards you, pitch will seem higher