Universal Wave Equation, Transverse and Longitudinal Waves

What is a vibration?

A vibration is a cyclical motion about an equilibrium point. (ex. windshield wipers and clock pendulum)

What is a wave? (3)

Waves are disturbances that transfer energy over a distance  without permanently transporting matter along with it.

What is a transverse wave?

A wave that oscillates matter in a perpendicular direction to the wave’s motion (or propagation)

ex.

• string in musical instruments

• wave dance move

• moving slinky in up and down motion

• water

• EM waves/ light

What is a longitudinal wave?

A wave that oscillates matter in a parallel direction to the wave’s motion (or propagation)

ex.

• sound oscillation of air molecules

• pushing sling back and forth

• earthquake motion

What is a mechanical wave?

A wave that requires a medium to move through or else it cannot exist.

• Can be transverse or longitudinal

ex.

• waves in the ocean (need water, the medium, to occur)

What is a medium?

• The material (solid, liquid, or gas) through which a wave travels

• The more rigid it it is the more efficient it is at transferring a vibration (solids > liquids > gases)

• However other factors such as temperature, density, and tension play a role in the medium’s ability to transmit vibrations

What are electromagnetic (EM) waves? (3)

A wave that moves through a vacuum (which is just empty space).

• Created as a result of vibrations between electric and magnetic fields.

• ALL EM waves are photons and move at the same speed (3 ×10⁸ ms^-1)

• Bightness/ intensity of light is proportional to wave amplitude

What is the electromagnetic spectrum?

A classification of the types of electromagnetic waves arranged by wavelength and frequency.

• Gamma rays, X rays, Ultraviolet, visible spectrum, Infrared, Microwave, Radio waves

What are the 8 components of a wave?

• cycle

• period (T)

• frequency (f)

• amplitude (A)

• wavelength (λ)

• crest

• through

• equilibrium position

What is a cycle?

One complete shape that starts and end at the same position (e.g. crest to crest)

What is is the period (T)?

The amount of time it takes for the cycle to occur.

• measured in seconds (s)

What is the frequency (f)?

The number of cycles that occur per second.

• measured in Hertz (Hz)

• 1 Hz = 1 cycle/ second

Note: Frequency is affected by the source; it is not affected by changes to the speed or wavelength

What is the relationship between period and frequency?

• T = t/N or time/ cycle

• f = N/t or cycle/ second

T = 1/f and f = 1/T (reciprocal relationship)

• where N is the number of cycles and t is the total time for N cycles

What is the amplitude (A)?

The maximum distance a particle moves from the the equilibrium position.

What is a wavelength (λ)?

The distance a cycle travels.

• measured in meter (m)

What are crest, troughs, and equilibrium position?

• Crest - highest point

• Through - lowest point

• Equilibrium position - central rest point when not disturbed by wave

What is the universal wave equation?

v = fλ or v = λ/T

Note: the velocity is dependent on the medium, and the frequency is dependent on the source

What is phase?

• The phase is the particles state at one moment in time

• The state can be completely described by its position and velocity

• Particles can be described to be in phase, out of phase, and opposite phase (anti-phase) - misaligned by exactly 180 degrees

What are 3 factors that affect wave speed?

• Temperature

• Molecular forces

• Tension (strings)

How does temperature affect wave speed?

• Waves travel faster in warmer gases

• Waves travel more slowly in colder gases

• Since molecules in hotter gases travel faster and transfer energy a lot more efficiently through collisions

• Temperature plays a role in the equation for the velocity of a sound wave:

  • v = 331.4 ms^-1 + 0.606 ms^-1°c^-1 (T)

    • where T is the object’s temperature in celcius

How does molecular forces affect wave speed?

• strong molecular forces = faster energy transfer = higher wave speed

• (solid > liquid > gas)

What are the 2 properties that affect the speed of a string?

• Linear density (µ) determines how much force it takes to make the string vibrate

  • Mass per unit length determines how much force is needed to vibrate a string

  • µ = m / L

• Tension in a string determines how well it transmits energy (a loose string quickly absorbs energy, whereas a tight string transmits energy very effectively)

  • v = square root (F_T / µ)

What does a displacement-distance graph tell you?

• Shows the displacement of all particles in the medium at one single, frozen moment in time (snapshot).

• Can find the wavelength

What does a displacement-time graph tell you?

• Shows how a single particle's displacement changes as time passes.

• Can find the period