Waves and Sound 14.1 Waves and Wave Pulses 14.2 Motion and Interaction of Waves 14.3 Natural Frequency and Resonance

Chapter 14 Objectives Recognize a wave in nature or technology. Measure or calculate the wavelength, frequency, amplitude, and speed of a wave. Give examples of transverse and longitudinal waves. Sketch and describe how to create plane waves and circular waves. Give at least one example of reflection, refraction, absorption, interference, and diffraction. Describe how boundaries create resonance in waves. Describe the relationship between the natural frequency, fundamental mode, and harmonics.

Chapter 14 Vocabulary Terms wave propagation amplitude frequency wavelength hertz (Hz) wave pulse transverse wave longitudinal wave oscillation crest trough wave front circular wave plane wave continuous fixed boundary open boundary reflection refraction absorption boundary condition incident wave reflected wave refracted wave standing wave superposition principle natural frequency resonance mode node constructive interference fundamental harmonic boundary interference destructive interference diffraction absorption antinode

14.1 Waves and Wave Pulses Key Question: What is the speed of a wave? *Students read Section 14.1 AFTER Investigation 14.1

14.1 Waves A wave is an oscillation that travels. A ball floating on water can oscillate up and down in harmonic motion. The surface of the water oscillates in response and the oscillation spreads outward from where it started.

14.1 Why learn about waves? Waves carry useful information and energy. Waves are all around us: light from the stoplight ripples in a puddle of electricity flowing in wires radio and television and cell phone transmissions

14.1 Recognize waves Anytime you see a vibration that moves... Anything that makes or responds to sound... Anything that makes or responds to light ... Anything that transmits information through the air (or space) without wires... cell phones, radio, and television. Anything that allows you to “see through” objects... ultrasound, CAT scans, MRI scans, and X rays

14.1 Characteristics of waves Waves have cycles, frequency, and amplitude, just like oscillations. The amplitude of a wave is the maximum movement from equilibrium. The frequency of a wave tells how often each point oscillates. The wavelength of a wave is the length of one complete cycle.

14.1 Wave pulses A wave pulse is a short length of wave, often just a single oscillation.

14.1 Relationship between speed, frequency, and wavelength The speed of a wave equals the frequency times the wavelength. Frequency (cycles/sec) Speed (m/sec) v = f l Wavelength (m)

14.1 Calculate wave speed A student does an experiment with waves in water. The student measures the wavelength of a wave to be 5 centimeters. By using a stopwatch and observing the oscillations of a floating ball, the student measures a frequency of 4 Hz. If the student starts a wave in one part of a tank of water, how long will it take the wave to reach the opposite side of the tank 2 meters away? 1) You are asked for the time it takes to move a distance of 2 meters. 2) You are given the frequency, wavelength, and distance. 3) The relationship between frequency, wavelength, and speed is v = fλ. The relationship between time, speed, and distance is v = d ÷ t. 4) Rearrange the speed formula to solve for the time: t = d ÷ v. The speed of the wave is the frequency times the wavelength. v = fλ = (4 Hz)(5 cm) = 20 cm/sec = 0.2 m/sec. Use this value to calculate the time: t = (2 m) ÷ (0.2 m/sec) = 10 seconds

14.1 Transverse and longitudinal waves A transverse wave has its oscillations perpendicular to the direction the wave moves. A longitudinal wave has oscillations in the same direction as the wave moves.

14.2 Motion and Interaction of Waves Key Question: How do waves move and interact with things? *Students read Section 14.2 AFTER Investigation 14.2

14.2 Waves in Motion Waves have crests and troughs. The crest of a wave is sometimes called a wave front. The shape of a wave is determined by its wave front.

14.2 Propagation of waves The word propagation means “to spread out and grow.” When you drop a stone into water, some of the water is pushed aside and raised up by the stone (A). The higher water pushes the water next to it out of the way as it tries to get back down to equilibrium (B). The water that has been pushed then pushes on the water in front of it, and so on. The wave spreads through the interaction of each bit of water with the water immediately next to it (C).

14.2 Propagation of waves Water waves propagate along surfaces that are continuous. A water wave can not spread across a discontinuous surface.

14.2 Waves and boundaries A boundary is a place where conditions change. What a wave does at a boundary depends on the boundary conditions. Waves can interact with boundaries in four different ways...

14.2 Waves and boundaries The wave approaching a boundary is called the incident wave. The wave sent from a boundary is the reflected wave. A wave that is bent passing through a boundary is called a refracted wave. This incident plane wave refracts a circular wave after passing through a convex barrier.

14.2 Waves and boundaries Boundaries that are not straight can be used to change the shape of the wave fronts and therefore change the direction of a wave. A sharp boundary creates strong reflections. A soft boundary absorbs wave energy and produces little reflection.

14.3 Natural Frequency and Resonance Key Question: How do we make and control waves? *Students read Section 14.3 AFTER Investigation 14.3

14.2 Superposition principle It is common for there to be many waves in the same system at the same time. When more than one wave is present, the total oscillation of any point is the sum of the oscillations from each individual wave. The sound waves and light waves you experience are the superposition of thousands of waves with different frequencies and amplitudes. Your eyes, ears, and brain separate the waves in order to recognize individual sounds and colors.

14.2 Interference If two waves add up to create a larger amplitude, constructive interference has occurred. In destructive interference, waves add up to make a smaller amplitude.

14.3 Natural Frequency and Resonance Waves can show natural frequency and resonance, just like oscillators. The natural frequency of a wave depends on the wave and also on the system that contains the wave. Resonance in waves is caused by reflections from the boundaries of a system.

14.3 Standing waves A wave that is confined between boundaries is called a standing wave. With all waves, resonance and natural frequency are dependent on reflections from boundaries of the system containing the wave.

14.3 Standing Waves and Harmonics The standing wave with the longest wavelength is called the fundamental. The fundamental has the lowest frequency in a series of standing waves called harmonics. The first three standing wave patterns of a vibrating string shows that patterns occur at multiples of the fundamental frequency.

14.3 Energy and Waves All waves propagate by exchanging energy between two forms. For water and elastic strings, the exchange is between potential and kinetic energy. For sound waves, the energy oscillates between pressure and kinetic energy. In light waves, energy oscillates between electric and magnetic fields.

14.3 Describing Waves Standing waves have nodes and antinodes. A node is a point where the string stays at its equilibrium position. An antinode is a point where the wave is as far as it gets from equilibrium.

14.3 Describing Waves A mode is a category of types of wave behavior. One mode of the vibrating string is a rotating wave and the other mode is a transverse wave. Because a vertical vibrating string moves in circles, the wave looks the same from the front and from the side.

14.3 Standing waves in 2 and 3 dimensions Most vibrating objects have more complex shapes than a string. Complex shapes create more ways an object can vibrate. Two- and three- dimensional objects tend to have two or three families of modes. A skillful drummer knows how and where to hit the drum to make mixtures of the different modes and get particular sounds. The radial modes have nodes and antinodes that are circles. The angular modes have nodes and antinodes that are radial lines from the center of the circle. A circular disc has two dimensions because you can identify any point on the surface with two coordinates (radius, angle).

Application: Microwave Ovens

15.1 Properties of Sound Key Question: What is sound and how do we hear it? *Students read Section 15.1 AFTER Investigation 15.1

15.1 Properties of Sound If you could see the atoms, the difference between high and low pressure is not as great. Here, it is exaggerated.

15.2 The frequency of sound We hear frequencies of sound as having different pitch. A low frequency sound has a low pitch, like the rumble of a big truck. A high-frequency sound has a high pitch, like a whistle or siren. In speech, women have higher fundamental frequencies than men.

15.1 Complex sound When we hear complex sounds, the nerves in the ear respond separately to each different frequency. The brain interprets the signals from the ear and creates a “sonic image” from the frequencies. The meaning in different sounds is derived from the patterns in how the different frequencies get louder and softer.

Common Sounds and their Loudness

15.1 Loudness Logarithmic scale Linear scale Decibels (dB) Amplitude 1 20 10 40 100 60 1,000 80 10,000 100,000 120 1,000,000 Every increase of 20 dB, means the pressure wave is 10 times greater in amplitude.

15.1 Sensitivity of the ear How we hear the loudness of sound is affected by the frequency of the sound as well as by the amplitude. The human ear is most sensitive to sounds between 300 and 3,000 Hz. The ear is less sensitive to sounds outside this range. Most of the frequencies that make up speech are between 300 and 3,000 Hz. The Equal Loudness Curve on the right shows how sounds of different frequencies compare. Sounds near 2,000 Hz seem louder than sounds of other frequencies, even at the same decibel level. For example, the Equal Loudness Curve shows that a 40 dB sound at 2,000 Hz sounds just as loud as an 80 dB sound at 50 Hz.

15.1 How sound is created The human voice is a complex sound that starts in the larynx, a small structure at the top of your windpipe. The sound that starts in the larynx is changed by passing through openings in the throat and mouth. Different sounds are made by changing both the vibrations in the larynx and the shape of the openings. The Equal Loudness Curve on the right shows how sounds of different frequencies compare. Sounds near 2,000 Hz seem louder than sounds of other frequencies, even at the same decibel level. For example, the Equal Loudness Curve shows that a 40 dB sound at 2,000 Hz sounds just as loud as an 80 dB sound at 50 Hz.

15.1 Recording sound A common way to record sound starts with a microphone. A microphone transforms a sound wave into an electrical signal with the same pattern of oscillation.

15.1 Recording sound In modern digital recording, a sensitive circuit converts analog sounds to digital values between 0 and 65,536.

15.1 Recording sound Numbers correspond to the amplitude of the signal and are recorded as data. One second of compact-disk-quality sound is a list of 44,100 numbers.

15.1 Recording sound To play the sound back, the string of numbers is read by a laser and converted into electrical signals again by a second circuit which reverses the process of the previous circuit.

15.1 Recording sound The electrical signal is amplified until it is powerful enough to move the coil in a speaker and reproduce the sound.

15.2 Sound Waves Key Question: Does sound behave like other waves? *Students read Section 15.2 BEFORE Investigation 15.2

15.2 Sound Waves Sound has both frequency (that we hear directly) and wavelength (demonstrated by simple experiments). The speed of sound is frequency times wavelength. Resonance happens with sound. Sound can be reflected, refracted, and absorbed and also shows evidence of interference and diffraction.

15.2 Sound Waves A sound wave is a wave of alternating high-pressure and low-pressure regions of air.

15.2 The wavelength of sound

15.2 The Doppler effect The shift in frequency caused by motion is called the Doppler effect. It occurs when a sound source is moving at speeds less than the speed of sound.

15.2 The speed of sound The speed of sound in air is 343 meters per second (660 miles per hour) at one atmosphere of pressure and room temperature (21°C). An object is subsonic when it is moving slower than sound.

15.2 The speed of sound We use the term supersonic to describe motion at speeds faster than the speed of sound. A shock wave forms where the wave fronts pile up. The pressure change across the shock wave is what causes a very loud sound known as a sonic boom.

15.2 Standing waves and resonance Spaces enclosed by boundaries can create resonance with sound waves. The closed end of a pipe is a closed boundary. An open boundary makes an antinode in the standing wave. Sounds of different frequencies are made by standing waves. A particular sound is selected by designing the length of a vibrating system to be resonant at the desired frequency.

15.2 Sound waves and boundaries Like other waves, sound waves can be reflected by surfaces and refracted as they pass from one material to another. Sound waves reflect from hard surfaces. Soft materials can absorb sound waves.

15.2 Fourier's theorem Fourier’s theorem says any complex wave can be made from a sum of single frequency waves.

15.2 Sound spectrum A complex wave is really a sum of component frequencies. A frequency spectrum is a graph that shows the amplitude of each component frequency in a complex wave.

15.3 Sound, Perception, and Music Key Question: How is musical sound different than other types of sound? *Students read Section 15.3 AFTER Investigation 15.3

15.3 Sound, Perception, and Music A single frequency by itself does not have much meaning. The meaning comes from patterns in many frequencies together. A sonogram is a special kind of graph that shows how loud sound is at different frequencies. Every person’s sonogram is different, even when saying the same word.

15.3 Hearing sound The eardrum vibrates in response to sound waves in the ear canal. The three delicate bones of the inner ear transmit the vibration of the eardrum to the side of the cochlea. The fluid in the spiral of the cochlea vibrates and creates waves that travel up the spiral.

15.3 Sound The nerves near the beginning see a relatively large channel and respond to longer wavelength, low frequency sound. The nerves at the small end of the channel respond to shorter wavelength, higher-frequency sound.

15.3 Music The pitch of a sound is how high or low we hear its frequency. Though pitch and frequency usually mean the same thing, the way we hear a pitch can be affected by the sounds we heard before and after. Rhythm is a regular time pattern in a sound. Music is a combination of sound and rhythm that we find pleasant. Most of the music you listen to is created from a pattern of frequencies called a musical scale.

15.3 Consonance, dissonance, and beats Harmony is the study of how sounds work together to create effects desired by the composer. When we hear more than one frequency of sound and the combination sounds good, we call it consonance. When the combination sounds bad or unsettling, we call it dissonance.

15.3 Consonance, dissonance, and beats Consonance and dissonance are related to beats. When frequencies are far enough apart that there are no beats, we get consonance. When frequencies are too close together, we hear beats that are the cause of dissonance. Beats occur when two frequencies are close, but not exactly the same.

15.3 Harmonics and instruments The same note sounds different when played on different instruments because the sound from an instrument is not a single pure frequency. The variation comes from the harmonics, multiples of the fundamental note.

Application: Sound from a Guitar