Properties of waves

Waves A Wave is the motion of disturbance. In a wave, particles vibrate with simple harmonic motion. Medium: a physical environment through which a disturbance can travel (Ex: water or air) Mechanical Waves: a wave that requires a medium through which to travel Sound waves can not travel through outer space. Electromagnetic Waves: do not need a medium to travel Ex: visible light, radio waves, ultraviolet, microwaves, Xrays

Relationship between shm and wave motion Sine Wave: a wave whose source vibrates with SHM. Name given from the graph of the trigonometric function: y=sin x If we focus on one point of the rope, we can see that it vibrates around its equilibrium position with SHM.

Measures of simple harmonic motion Amplitude – the maximum displacement from equilibrium. Units: meters Period – the time that it takes a complete cycle to occur. Symbol: T Units: seconds Frequency – number of cycles or vibrations per second Symbol: f Units: hertz (Hz), 𝟏 𝒔 , s-1 Wavelength – distance between 2 crests or 2 troughs Symbol: λ (lambda) Units: m, nm

Transverse Waves Transverse Wave: a wave whose particle vibrate perpendicularly to the direction the wave is traveling.

Longitudinal Wave Longitudinal Wave: a wave whose particles vibrate parallel to the direction the wave is traveling.

𝑻= 𝟏 𝒇 𝒗=𝒇𝝀 Wave Equations T= Period [s] v= speed [m/s] 𝑻= 𝟏 𝒇 𝒗=𝒇𝝀 T= Period [s] v= speed [m/s] f= frequency [ 𝑠 −1 ] f= frequency [ 𝑠 −1 ] λ=wavelength [m]

𝐸𝑛𝑒𝑟𝑔𝑦= 𝐴𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 2 (mechanical waves) Wave travel Waves transfer energy through vibration. The greater the amplitude, the more energy a wave carries in a given time interval. 𝐸𝑛𝑒𝑟𝑔𝑦= 𝐴𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 2 (mechanical waves)

Practice A spring-block oscillator oscillates with a period of 2.5 seconds. What is its frequency?

Practice A piano string tuned to middle C vibrates with a frequency of 262 Hz. Assuming the speed of sound in air is 343 m/s, find the wavelength of the sound waves produced by the string.