Introduction to Mechanical Waves Types of Waves and Wave Properties

Mechanical Waves What is a mechanical wave? What is the medium? A mechanical wave is a rhythmic disturbance that allows energy to be transferred through matter because of the motion of and interactions between the particles in the matter What is the medium? The medium is the general term for the actual matter through which the wave is traveling. What is wave propagation ? Wave propagation is the term given when describing the transfer of energy through a medium

Sketch In Your Journal It should be at least a ½ page Leave plenty of room for labeling and definitions

Types of Waves Transverse Waves: A wave in which the energy is transferred in a direction perpendicular to the direction of particle movement This type of wave is typically only found in solids Example: Earthquake S - Waves, Guitar Strings

Direction of Particle Motion Transverse Waves A wave in which the energy is transferred in a direction perpendicular to the direction of particle movement: Direction of wave propagation Direction of Particle Motion

Transverse Wave Properties Amplitude (A): the maximum displacement of a particle in the medium from its rest position: Direction of wave propagation Direction of Particle motion Amplitude (A)

Transverse Wave Properties Trough: The point in a wave cycle where the medium has reached the maximum displacement BELOW the rest position: Direction of wave propagation Direction of Particle Motion Amplitude Amplitude (A) Trough

Transverse Wave Properties Crest: The point in a wave cycle where the medium has reached the maximum displacement ABOVE the rest position: Direction of wave propagation Direction of Particle Motion Amplitude Trough Crest Amplitude (A)

Transverse Wave Properties Wavelength (λ): The distance from one point on a wave to the same point on the next wave (i.e. the distance from crest to crest): Direction of wave propagation Direction of Particle Motion Amplitude (A) Trough Crest Wavelength (λ)

Transverse Wave Properties Direction of wave propagation Direction of Particle Motion Amplitude (A) Trough Crest Wavelength (λ)

Sketch In Your Journal It should be at least a ¼ page Leave plenty of room for labeling and definitions

Another Type of Wave Longitudinal or compression wave: A wave in which the energy is transferred in a direction parallel to the direction of particle movement Can be present in solids, liquids, or gases Example: Sound Waves, Earthquake P-Waves

Direction of Particle Motion Longitudinal Waves A wave in which the energy is transferred in a direction parallel to the direction of particle movement: Direction of wave propagation Direction of Particle Motion

Longitudinal Wave Properties Compression: The location in the medium of the greatest particle density and highest pressure: Direction of wave propagation Compression Direction of Particle Motion

Longitudinal Wave Properties Rarefaction: The location in the medium with the lowest particle density and lowest pressure: Direction of wave propagation Compression Rarefaction Direction of Particle Motion

Longitudinal Wave Properties The wavelength (λ) of a longitudinal wave is typically measured from the beginning of one compression to the beginning of the next (or center to center) Direction of wave propagation Wavelength (λ) Compression Rarefaction Direction of Particle Motion

Longitudinal Wave Properties Direction of Particle Motion Direction of wave propagation Compression Rarefaction Wavelength (λ)

Surface Waves Surface waves are waves that have characteristics of both transverse and longitudinal waves Medium particles move both parallel to and perpendicular to wave propagation Resulting path of particles’ motion is circular Examples: Water Waves, Earthquakes

Quantitative Wave Characteristics Wave Frequency ( f ): The number of complete wave cycles that pass by a point every second Units = Hertz (Hz) = 1 (1/sec) = 1 sec-1 Period (T): The amount of time that it takes for one complete wave cycle to pass by a point Units = Seconds (s) By definition, the frequency and the period of a wave are the inverse of each other: 𝒇= 𝟏 𝑻

Wave Speed Wave speed (v): Speed of a wave will be constant in a given medium What is our definition of speed? 𝑣= 𝑑 𝑡 What do we call the distance a wave travels? Wavelength (λ) What do we call the time it takes to travel 1 wavelength? Period (T)

𝑤𝑎𝑣𝑒 𝑠𝑝𝑒𝑒𝑑= 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ 𝑝𝑒𝑟𝑖𝑜𝑑 Wave Speed Wave speed (v): 𝑣= 𝑑 𝑡 Distance (d) = wavelength (λ) Time (t) = period (T) 𝑤𝑎𝑣𝑒 𝑠𝑝𝑒𝑒𝑑= 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ 𝑝𝑒𝑟𝑖𝑜𝑑 𝒗= 𝝀 𝑻 or 𝒗=𝒇∙𝝀

Practice Problem 1 A surfer is waiting for the perfect waves. While waiting, the surfer notices that 7 waves pass by every minute. What is the period of one of the water waves? What is the frequency of the wave?

Practice Problem 1a 𝑻 𝒐𝒏𝒆 𝒘𝒂𝒗𝒆 =𝟖.𝟓 𝒔 A surfer is waiting for the perfect waves. While waiting, the surfer notices that 7 waves pass by every minute. What is the period of one of the water waves? 𝑇 𝑜𝑛𝑒 𝑤𝑎𝑣𝑒 = 𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 # 𝑜𝑓 𝑤𝑎𝑣𝑒𝑠 𝑇 𝑜𝑛𝑒 𝑤𝑎𝑣𝑒 = 60 s 7 waves 𝑻 𝒐𝒏𝒆 𝒘𝒂𝒗𝒆 =𝟖.𝟓 𝒔

Practice Problem 1b 𝒇=𝟎.𝟏𝟐 𝐇𝐳 A surfer is waiting for the perfect waves. While waiting, the surfer notices that 7 waves pass by every minute. What is the frequency of the wave? 𝑓= 1 𝑇 𝑓= 1 8.5 s 𝒇=𝟎.𝟏𝟐 𝐇𝐳

Practice Problem 2 The surfer has drifted 65 meters from shore. It takes the surfer 25 seconds to ride a wave back to shore. What is the wave speed for the water wave? 𝑣= 𝑑 𝑡 𝑣= 65 m 25 s 𝒗=𝟐.𝟔 𝐦 𝐬

Practice Problem 3 Using what we know about the surfer’s last wave of the day: What is the wavelength of the ocean wave? 𝑣=𝑓𝜆 𝜆= 𝑣 𝑓 𝜆= 2.6 m 𝑠 0.12 Hz 𝝀=𝟐𝟐 𝐦

Mechanical Waves Demo Notes On the demo note handout: PREDICT for Demos 1 - 3 Write down your observations after each demo. Write a brief summary about the “take home message” for each video demo!