Physics of Periodic Motion, Waves, and Resonance: Key Concepts and Formulas

What is periodic motion?

Motion that repeats over and over in a regular pattern.

What is simple harmonic motion (SHM)?

Repeating back-and-forth motion around an equilibrium position.

What is the equilibrium position?

The middle/resting position of an object.

What is amplitude (A)?

The maximum distance an object moves from its equilibrium position.

What is the period (T)?

The time it takes to complete one full cycle, measured in seconds (s).

What is frequency (f)?

The number of complete cycles that happen each second, measured in Hertz (Hz).

What is the relationship between frequency and period?

f = 1/T

How do you find period from frequency?

T = 1/f

What does F mean in Hooke's Law?

Spring force, measured in Newtons (N).

What does k mean in Hooke's Law?

Spring constant, which tells how stiff the spring is.

What does x mean in Hooke's Law?

The displacement from the equilibrium position, measured in meters.

Why is there a negative sign in F = -kx?

The spring force points back toward the equilibrium position.

What is the period of a mass-spring system?

T = 2π√(m/k)

What happens to the period when mass increases?

The period gets longer.

What happens to the period when the spring gets stiffer?

The period gets shorter.

What is a pendulum?

An object hanging from a fixed point that swings back and forth.

What is the period of a pendulum?

T = 2π√(L/g)

Does a pendulum's period depend on mass?

No, the mass of the bob does not affect the period.

What does a pendulum's period depend on?

The length of the pendulum and gravity.

What happens when pendulum length increases?

The period gets longer.

What happens when pendulum length decreases?

The period gets shorter.

What is the value of gravitational acceleration (g)?

Approximately 9.8 m/s².

What is a wave?

A disturbance that transfers energy from one place to another.

What is wavelength (λ)?

The distance between matching points on consecutive waves, such as crest-to-crest.

What is a crest?

The highest point of a transverse wave.

What is a trough?

The lowest point of a transverse wave.

What is wave frequency?

The number of complete waves that pass a point each second.

What is the wave speed equation?

v = fλ

What is the speed equation?

v = d/t

What does v mean in v = fλ?

Wave speed, measured in meters per second (m/s).

What does f mean in v = fλ?

Frequency, measured in Hertz (Hz).

What does λ mean in v = fλ?

Wavelength, measured in meters (m).

What is a transverse wave?

A wave where particles move perpendicular to the direction the wave travels.

What is an example of a transverse wave?

A wave traveling along a rope.

What is a longitudinal wave?

A wave where particles move back and forth parallel to the direction the wave travels.

What is an example of a longitudinal wave?

Sound waves.

What is compression in a wave?

An area of a longitudinal wave where particles are close together.

What is rarefaction in a wave?

An area of a longitudinal wave where particles are spread apart.

What is a surface wave?

A wave that combines transverse and longitudinal motion.

What is an example of a surface wave?

Ocean waves.

What is constructive interference?

When two waves combine to make a larger wave.

What is destructive interference?

When two waves combine and partially or completely cancel each other.

What is a standing wave?

A wave pattern that appears to stay in one place.

What is a node?

A point on a standing wave that does not move.

What is an antinode?

A point on a standing wave with the maximum movement.

What is pitch?

How high or low a sound sounds.

What determines pitch?

Frequency.

What happens to pitch when frequency increases?

Pitch increases.

What happens to pitch when frequency decreases?

Pitch decreases.

What is the Doppler effect?

The change in observed frequency caused by motion between the source and observer.

What happens in the Doppler effect when a source approaches?

Higher observed frequency and higher pitch.

What happens in the Doppler effect when a source moves away?

Lower observed frequency and lower pitch.

What is resonance?

When an object is forced to vibrate at or very close to its natural frequency, causing a large amplitude.

What conditions are needed for resonance?

The driving frequency must be equal or very close to the object's natural frequency.

What is a closed-pipe resonator?

A pipe closed on one end and open on the other.

What is the closed-pipe fundamental relationship?

L = λ/4

What is an open-pipe resonator?

A pipe that is open on both ends.

What is the open-pipe fundamental relationship?

L = λ/2

Does amplitude affect wave energy?

Yes, a larger amplitude means more energy is carried by the wave.

What is the difference between frequency and period?

Frequency tells how many cycles happen per second; period tells how long one cycle takes.

If frequency increases, what happens to period?

Period decreases.

If frequency decreases, what happens to period?

Period increases.

Can wave speed in a spring change?

Yes, it can change if properties such as the spring's tension or mass per length change.

Can frequency of a wave in a spring change?

Yes, the source can change the frequency.

If wave speed stays constant and frequency increases, what happens to wavelength?

Wavelength decreases.

If wave speed stays constant and frequency decreases, what happens to wavelength?

Wavelength increases.