1 The Nature of Waves Water waves are partially transverse and partially longitudinal.
2 Periodic Waves Periodic waves consist of cycles or patterns that are produced over and over again by the source. In the figures, every segment of the slinky vibrates in simple harmonic motion, provided the end of the slinky is moved in simple harmonic motion.
2 Periodic Waves In the drawing, one cycle is shaded in color. The amplitude A is the maximum excursion of a particle of the medium from the particles undisturbed position. The wavelength is the horizontal length of one cycle of the wave. The period is the time required for one complete cycle. The frequency is related to the period and has units of Hz, or s -1.
Example 1 The Wavelengths of Radio Waves AM and FM radio waves are transverse waves consisting of electric and magnetic field disturbances traveling at a speed of 3.00x10 8 m/s. A station broadcasts AM radio waves whose frequency is 1230x10 3 Hz and an FM radio wave whose frequency is 91.9x10 6 Hz. Find the distance between adjacent crests in each wave.
3 Wave Speed Versus Particle Speed on a String Conceptual Example 3 Wave Speed Versus Particle Speed Is the speed of a transverse wave on a string the same as the speed at which a particle on the string moves?
4 The Nature of Sound Waves LONGITUDINAL SOUND WAVES
4 The Nature of Sound Waves The distance between adjacent condensations is equal to the wavelength of the sound wave.
4 The Nature of Sound Waves Individual air molecules are not carried along with the wave.
4 The Nature of Sound Waves THE FREQUENCY OF A SOUND WAVE The frequency is the number of cycles per second. A sound with a single frequency is called a pure tone. The brain interprets the frequency in terms of the subjective quality called pitch.
Check your Hearing https://www.youtube.com/watch?v=qNf9nzvnd1k https://www.youtube.com/watch?v=VxcbppCX6Rk
4 The Nature of Sound Waves THE PRESSURE AMPLITUDE OF A SOUND WAVE Loudness is an attribute of a sound that depends primarily on the pressure amplitude of the wave.
4 The Speed of Sound Sound travels through gases, liquids, and solids at considerably different speeds.
4 The Speed of Sound Conceptual Example 5 Lightning, Thunder, and a Rule of Thumb There is a rule of thumb for estimating how far away a thunderstorm is. After you see a flash of lighting, count off the seconds until the thunder is heard. Divide the number of seconds by five. The result gives the approximate distance (in miles) to the thunderstorm. Why does this rule work?
1. What is the wave speed if the period of a wave is 4 seconds and the wavelength is 1.8 m? 2 A fisherman noticed that a float makes 30 oscillations in 15 seconds. The distance between to consecutive crests is 2 m. What is the wave speed?
3 What is the wavelength of a wave traveling with a speed of 6 m/s and a period of 3s? 4. What is the period of a wave traveling with a speed of 20 m/s and the wavelength is 4.0 m? 5. What is the wave speed if the period is 4.0 seconds and the wavelength is 1.8 m?
5 The Doppler Effect The Doppler effect is the change in frequency or pitch of the sound detected by an observer because the sound source and the observer have different velocities with respect to the medium of sound propagation.
5 The Doppler Effect source moving toward a stationary observer source moving away from a stationary observer
5 The Doppler Effect Example 10 The Sound of a Passing Train A high-speed train is traveling at a speed of 44.7 m/s when the engineer sounds the 415-Hz warning horn. The speed of sound is 343 m/s. What are the frequency and wavelength of the sound, as perceived by a person standing at the crossing, when the train is (a) approaching and (b) leaving the crossing?
6. Standing wave Wave reflection at boundaries Principle of superposition, interference Standing waves on a string Normal modes
Reflection of a wave pulse at a boundary Fixed end Free end Pulse incident from right is reflected from the boundary at left HOW the pulse is reflected depends on the boundary conditions For fixed end, reflected pulse is inverted For free (in transverse direction) end, reflected pulse is same way up. time Frictionless sliding ring Check using phet simulation
Reflection of a wave pulse at a boundary Behaviour at interface can be modelled as sum of two pulses moving in opposite directions at the interface: Transverse displacement always 0 at interface “fixed end” “free end” Transverse force always 0 at interface
Standing Waves A standing wave is produced when a wave that is traveling is reflected back upon itself. There are two main parts to a standing wave: Antinodes – Areas of MAXIMUM AMPLITUDE Nodes – Areas of ZERO AMPLITUDE.
Comparison between standing wave and travelling wave Travelling wave particles undergo SHM all particles have same amplitude all particles have same frequency, adjacent particles have different phase Standing wave particles undergo SHM adjacent particles have different amplitude all particles have same frequency all particles on same side of a node have same phase. Particles on opposite sides of node are in antiphase
Some very basic physics of stringed instruments……….
The fundamental frequency determines the pitch of the note. the higher harmonics determine the “colour” or “timbre” of the note. (ie why different instruments sound different)
Fundamental wavelength = 2L From v = fλ, f 1 = v/2L So, for a string of fixed length, the pitch is determined by the wave velocity on the string…..
Example Calculation The string length on standard violin is 325mm. What tension is required to tune a steel “A” string (diameter =0.5mm) to correct pitch (f=440Hz)? Density of steel = 8g cm
Sound Waves The production of sound involves setting up a wave in air. To set up a CONTINUOUS sound you will need to set a standing wave pattern. Three LARGE CLASSES of instruments Stringed - standing wave is set up in a tightly stretched string Percussion - standing wave is produced by the vibration of solid objects Wind - standing wave is set up in a column of air that is either OPEN or CLOSED Factors that influence the speed of sound are density of solids or liquid, and TEMPERATURE
Closed Pipes Have an antinode at one end and a node at the other. Each sound you hear will occur when an antinode appears at the top of the pipe. What is the SMALLEST length of pipe you can have to hear a sound? You get your first sound or encounter your first antinode when the length of the actual pipe is equal to a quarter of a wavelength. This FIRST SOUND is called the FUNDAMENTAL FREQUENCY or the FIRST HARMONIC.
Closed Pipes - Harmonics Harmonics are MULTIPLES of the fundamental frequency. In a closed pipe, you have a NODE at the 2nd harmonic position, therefore NO SOUND is produced
Closed Pipes - Harmonics In a closed pipe you have an ANTINODE at the 3rd harmonic position, therefore SOUND is produced. CONCLUSION: Sounds in CLOSED pipes are produced ONLY at ODD HARMONICS!
Open Pipes OPEN PIPES- have an antinode on BOTH ends of the tube. What is the SMALLEST length of pipe you can have to hear a sound? You will get your FIRST sound when the length of the pipe equals one-half of a wavelength.
Open Pipes - Harmonics Since harmonics are MULTIPLES of the fundamental, the second harmonic of an “open pipe” will be ONE WAVELENGTH. The picture above is the SECOND harmonic or the FIRST OVERTONE.
Open pipes - Harmonics Another half of a wavelength would ALSO produce an antinode on BOTH ends. In fact, no matter how many halves you add you will always have an antinode on the ends The picture above is the THIRD harmonic or the SECOND OVERTONE. CONCLUSION: Sounds in OPEN pipes are produced at ALL HARMONICS!
Example The speed of sound waves in air is found to be 340 m/s. Determine the fundamental frequency (1st harmonic) of an open-end air column which has a length of 67.5 cm. 251.85 HZ
Example The windpipe of a typical whooping crane is about 1.525-m long. What is the lowest resonant frequency of this pipe assuming it is a pipe closed at one end? Assume a temperature of 37°C. 353.2 m/s 57.90 Hz
Resonance demo https://www.youtube.com/watch?v=1K5p9DfsXGo Destructive: https://www.youtube.com/watch?v=j-zczJXSxnw Sound wave energy on water: “Sound,Bass,Water, Sound makes water come alive with cymatics” Wave with Bill Nye https://www.youtube.com/watch?v=YsKC_EtUHcA “Bill Nye The Science Guy & Waves & Full Episode”
16.10 Applications of Sound in Medicine By scanning ultrasonic waves across the body and detecting the echoes from various locations, it is possible to obtain an image.
16.10 Applications of Sound in Medicine Ultrasonic sound waves cause the tip of the probe to vibrate at 23 kHz and shatter sections of the tumor that it touches.
16.10 Applications of Sound in Medicine When the sound is reflected from the red blood cells, its frequency is changed in a kind of Doppler effect because the cells are moving.