Vibrations and Waves Physics – 5 th 6wks

1. Vibrations and WavesPhysics – 5th 6wks

2. Waves & Vibration: Introduction • Vibration – a repeated back-and-forth motion, around a fixed position. (a wiggle in time) • Wave – a rhythmic disturbance that transfers energy through matter or space. • A wave is the physical effect of the movement of energy. • A wave exists only as long as it has energy to carry. • The source of all waves is something that vibrates (or wiggles if you will) Mythbusters - Metal Fusion Shockwave – YouTube Russian Meteorite Blast Wave Impact Nuclear Blast Wave from 1950s era High Speed of Massive Gunpowder Explosion

3. Period, Cycle, and Simple Harmonic Motion • Each complete vibration is known as a cycle. • Period – the time required to complete one cycle. • A reoccurring, back and forth motion (like that of a swinging pendulum) is called simple harmonic motion. Simple harmonic (or periodic) motion

4. Transverse Waves • Transverse Waves – waves in which the motion of the medium (what the wave is traveling through) is at right angles to the direction that the wave is moving. • Waves on the surface of liquids, stretched musical strings, and the different forms of light are transverse waves. • A pendulum that is undergoing simple harmonic motion, would trace out a transverse wave in its movement.

5. Parts of a Transverse Wave • The high points on a wave (the peaks) are known as crests. • The low points on a wave are called troughs. • The midpoint of the vibration, often represented by a dashed line, is called the point of equilibrium. Point of equilibrium or the midpoint

6. Parts of a Transverse Wave • Amplitude is the distance from the midpoint, or point of equilibrium and either the crest or trough of the wave. • The amplitude then equals the maximum displacement from equilibrium. • The greater energy that a wave has, the greater its amplitude is. • The wavelength of a wave is the distance from the top of one crest to the top of the next one. • The wavelength, to put simply, is the distance between two identical parts of a wave. Point of equilibrium or the midpoint

7. Longitudinal Waves • Sometimes the particles of the medium move back and forth in the same direction in which the wave travels. • Longitudinal Waves – waves in which the particles move along the direction of the wave rather than at right angles to it. • Also known as Compressional Waves or Mechanical Waves. • Sound Waves are longitudinal waves. • sound waves and a Rubens Tube • Rubens Tube and basic tones

8. Longitudinal Waves • The dense, compressed area of a longitudinal wave is called a Compression. • The lower density region of a longitudinal wave is called a Rarefaction. • The wavelength is measured either between two compressions or two rarefactions. • The more dense the medium becomes upon compression, the greater the longitudinal wave’s amplitude.

9. Parts of a Longitudinal Wave rarefaction wavelength compression

10. Ruben’s Tube & Sound Waves Rarefaction                         Compression                         A Rubens’ Tube is a metal tube sitting horizontally with tiny holes drilled in a line along the top. One end of the Rubens’ Tube is connected to a small tank of propane like those used when camping, and the other end of the Tube is connected to a speaker. When a sound is played through the speaker, the wave of energy compresses the propane gas inside of the tube and propane escapes out of the tiny holes on top. If the gas coming out of the holes is ignited, the flames will be taller where the gas is compressed and shorter where the gas particles are less dense. 

11. Waves through Water • Note waves of energy through water can behave like longitudinal • waves in the water and as transverse waves on the surface where the • water meets the air.

12. Earthquake/Seismic Waves • Earthquakes move as a combination of the two – as • P waves (pressure waves – or longitudinal) and S Waves (transverse waves). Matter tends to move in an elliptical pattern as the waves of energy move through the ground

13. Frequency • How often a vibration occurs is described by its frequency • One back and forth motion would be a cycle. • If this happened in one second, the frequency would be 1 cycle per second. If two vibrations happened in 1 second, the frequency would be 2 cycles per second, etc. • The unit for frequency is called the Hertz (named after the German scientist Heinrich Hertz who was the first to produce & receive radio waves) and its symbol is Hz • A frequency of 1 cycle per second is equal to 1 Hz and a frequency of 2 cycles per second is equal to 2 Hz , and so on.

14. The relationship between Period and Frequency • If the frequency of a vibrating object is known, its period can be calculated, and vice versa. • If something vibrates twice in 1 second, its frequency is 2 Hz . Therefore, the time it took for one vibration to occur was ½ second. • If the frequency of an object was 3 Hz, then the period or time for one vibration to occur would be 1/3 sec . • The period then is the reciprocal of the frequency and the frequency is the reciprocal of the period. • Note: raising anything to the negative one power is the same as finding its reciprocal (or dividing it into 1) Note: Frequency is in Hz Period is in seconds

15. Circle diagram for the relationship between Period & Frequency of a Wave or Vibration 1 T F = 1 T F T Units: Period = seconds Frequency = Hz T = Period (of time) F= Frequency Remember: that is the same as doing

16. Example Problem 1: Period from Frequency If something vibrated 30 times every second (meaning it had a frequency of 30 Hz) how long did it take it to vibrate once? take the inverse of 30 Hz (or 30/sec) Period = Period = sec Period

17. Example Problem 2: Frequency from the Period If something vibrated once every 0.25 sec, at what frequency did it vibrate at? take the inverse of 0.25 sec Frequency = Frequency = 4 Hz that is, 4 times every second

18. Wave Speed • Speed, frequency, and wavelength of a wave are related. • In the formula for wave speed, speed is v, frequency is f, and wavelength is the Greek letter Lambda - λ • The units for wave speed are always a derived unit of distance divided by time. • If the wavelength between two crests of waves on the ocean is 3 meters, and 2 crests pass by a stationary point each second, then the wave speed is 3 meters x 2 cycles/second = 6 meters/second. Note: frequency will be in Hz, wave speed will be in m/s, and wavelength will be in m

19. Circle diagram for the Wave Speed formula v λ f = v λ f λ v = wave speed λ = wavelength f= frequency Units: Wave Speed = meters/second Frequency = Hz Wavelength = meters

20. Example Problem #3: Finding Wave Speed The frequency of a wave is 40 Hz, and the wavelength of the wave is 0.8m. What is the speed of the wave? v = 32 m/s

21. Example Problem #4: Finding wavelength The speed of a sound wave is 343 m/s and has a frequency of 500 Hz. What is the length of the wavelength? λ λ λ λ λ = 0.686 m

22. Example Problem #5: Finding the frequency The wavelength of a wave is 0.002 m and it has a wave speed of 0.05 m/s. What is the frequency of that wave? f = f = f f = 25/second f = 25 Hz