Wave Motions and Sound

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1 EA Notes (Scen 101), Tillery Chapter 5 Wave Motions and Sound Introduction Microscopic molecular vibrations determine temperature (last Chapt.). Macroscopic vibrations of objects set up what we call Sound waves. Waves move through space and carry energy away from the source. Several concepts depend on wave motion. (Wave Types) This chapter: Mechanical Waves: Elastic Materials & Sound. In later chapter: Electromagnetic Waves (EM): Radio, TV, Light, etc. EA Lec Notes (Scen 101) Til6Ed-Chap5-1 - Printed 03/30/2006, 1:18 PM

2 Forces and Elastic Materials Elastic Material: Deformation and Force are proportional to each other. Completely recovers its shape after a force has deformed it. ( Demo Orange Slinky ) Can be compressed as well as stretched. EA Lec Notes (Scen 101) Til6Ed-Chap5-2 - Printed 03/30/2006, 1:18 PM

3 Forces and Vibrations Vibration: ( Demo Coil Slinky ) A back-and-forth motion that repeats itself. ALL elastic SOLIDS can be made to vibrate. Equilibrium Position: ( Demo Coil Slinky On Board ) Rest Position. Where it would be if not vibrating. Displacement: ( Demo Coil Slinky On Board ) How far from equilibrium position at any moment. Periodic Motion: ( Demo SAW [vs. time] On Board ) Any motion that repeats itself exactly without stopping. Simple Harmonic Motion (SHM): Motion in which restoring force is opposite and proportional to displacement. Covers a lot of situations. ( Including Elastic Materials ) DEMO G r a p h : Sinusoidal Curve. ( Fig.5.4 vs time ) Used to graph SHM (Simple Harmonic Motion). EA Lec Notes (Scen 101) Til6Ed-Chap5-3 - Printed 03/30/2006, 1:18 PM

4 Describing Vibrations Amplitude: ( Demo WAVE Fig.5.4 ) MAXIMUM displacement from Equilibrium Position. Cycle: ( Demo Coil Slinky ) One complete vibration. Period: ( Demo WAVE Fig.5.4 ) Time for one cycle. Symbol: T, Units: [s]. Frequency: ( Demo Coil Slinky ) Number of cycles per second. Symbol: f, Units: [Hz]. ( Has dimensions of 1/s ) f 1 T T 1 f EA Lec Notes (Scen 101) Til6Ed-Chap5-4 - Printed 03/30/2006, 1:18 PM

5 Waves A Vibrating Source disturbs its surroundings. This disturbance, not the vibrating molecules themselves, travels away from the source. Propagation Speed depends on: Wave Type, Mechanical or Electromagnetic and Material in which it is propagating. The disturbance carries energy away from the source. WAVE IS: A traveling disturbance that transports energy. Wave energy propagates faster than disturbed "particles" can move. Propagation Direction: Direction in which wave is traveling. Most waves spread out radially from their source. Mechanical Wave: (This Chapter) Must have molecules (matter) for propagation. Transports KE away from source. EA Lec Notes (Scen 101) Til6Ed-Chap5-5 - Printed 03/30/2006, 1:18 PM

6 Vibrational Kinds of Waves Two Major Classifications, depending on whether vibrations are parallel or perpendicular to propagation direction. Figure 5.5 on p.119 shows both of these. DEMO Slinky? KIND of Mechanical Wave VIBRATION PHASES OF MATTER EXAMPLE Longitudinal Parallel All Sound Transverse Perpendicular Solid ONLY Taut String (Combination) Solid, Liquid (Liquid Surface; Earthquake) EA Lec Notes (Scen 101) Til6Ed-Chap5-6 - Printed 03/30/2006, 1:18 PM

7 Waves in Air (must be Longitudinal) Terms Compression: Extra Molecules jammed together. This is a commoner term than "condensation" used in text. Rarefaction: Thinned out Molecules. DEMO F o l d e r? Hearing Sound Waves in Air Source: Vibration (with KE) starts a wave in surrounding matter. Mechanical Vibrations compress and rarefy the surrounding air. This KE propagates outward. Waves reach eardrum and set it vibrating at same frequency. Normal Human Hearing Range: vibrations from 20 to 20,000 Hz. Infrasonic: Below 20 Hz. Ultrasonic: Above 20,000 Hz. Pitch: The brain's interpretation of sound frequency. EA Lec Notes (Scen 101) Til6Ed-Chap5-7 - Printed 03/30/2006, 1:18 PM

8 More Terms Describing Waves We've already defined: amplitude, cycle, period, and frequency. Figures 5.9-A & B (p.121): label the horizontal axes "distance." These parts show sound waves propagating in air. Figure 5.9-C (p.121): label the horizontal axis "time." Part shows sound wave vibrating in TIME at a fixed point in space. Figure 5.10 (p.123): horizontal axis is "(propagation) distance." Sound wave vibrating in SPACE at a fixed time. ("snapshot") Crest: Highest Point. Maximum Compression. Trough: Lowest Point. Maximum Rarefaction. Distance between two identical wave points. Wavelength: ( v = speed fixed by Wave Type, Material ) f Wave Eqn (Derive?) v v f REMEMBER: Sources produce frequency. Wavelength is: Do Ex. B-14, p.138. EA Lec Notes (Scen 101) Til6Ed-Chap5-8 - Printed 03/30/2006, 1:18 PM

9 Sound Waves Longitudinal wave in which molecules interact in sequence down line. Thus it needs a "medium" (substance) for its transmission. Speed of sound depends on the Material of the medium and its Physical Conditions, such as temperature. Typical Values in Table 5.1, p.124. (Sequence: Gas, Liquid, Solid.) Speed (Velocity) of Sound in Air Don' t Use v T [m s] Use ONLY this: v 20 C T [ 343 m s C] EA Lec Notes (Scen 101) Til6Ed-Chap5-9 - Printed 03/30/2006, 1:18 PM

10 Refraction and Reflection These concepts apply to ALL Wave Types (Mechanical and E-M). DEMO D r a w : Point source, a few rays. Wavefront: As wave spreads, the parts emitted from the source at same time can always be identified (and marked). Smooth curve drawn through these points is called a "wavefront". If source small compared to distance, spherical wavefronts. As distance gets very large, sphere gets close to a flat plane. Boundary: Boundary is the separation between different materials or different physical conditions in the same material. EA Lec Notes (Scen 101) Til6Ed-Chap Printed 03/30/2006, 1:18 PM

11 Refraction: Occurs because Wave Speed differs across boundary. Different parts of wavefront travel at different speeds. The faster the speed, the further the part travels each time unit. Result is a bending of the path as wave crosses boundary. Reflection: Occurs only at boundary between different materials. Part of the energy is reflected back into the first material, part passes into the second material, (and some may be absorbed). energy in energy reflected Reverberation: (sound wave only) transmitted absorbed. Reflected sound that returns to the ear before 0.1 sec. EA Lec Notes (Scen 101) Til6Ed-Chap Printed 03/30/2006, 1:18 PM

12 Interference A PROPERTY OF WAVES (or wave pulses) ONLY (not particles, not even the particles that are vibrating in the wave). Waves of the same type can exist in the same place at the same time. When they do, the effects of their individual disturbances add algebraically to a new disturbance. See Fig.5.15, p.127: As pulses cross the same place, they reinforce Constructively or cancel Destructively. After crossing, they have their original shape. Destructive Interference between sound waves leads to "dead spots". Beats: Fig.5.16, p.128: The horizontal axis is time. Two waves of slightly different frequencies hit a detector. The sound gets fainter and louder at the "beat frequency". Beat Frequency: f b f 2 f 1 Musical instruments are "tuned" by listening for zero beats. EA Lec Notes (Scen 101) Til6Ed-Chap Printed 03/30/2006, 1:18 PM

13 Energy and Sound W E t The energy passing a point per second is the power. P P A [W m2 ] Intensity, the power per unit area is more useful. I Loudness The brain's interpretation of the intensity of a sound wave. 1 W m 2. to I 12 W m Human ear can hear from I The brain interprets changes in intensity logarithmically. The scale used is called the "decibel scale". (Table 5.2 on p.129.) 0 db is at the threshold of hearing. each time you multiply the intensity by 10, you add 10 to the db scale. ( Mult by 100 adds 20, etc.) each time you divide the intensity by 10, you subtract 10 from the db scale. ( Div by 100 subtracts 20 ) EA Lec Notes (Scen 101) Til6Ed-Chap Printed 03/30/2006, 1:18 PM

14 Resonance All objects have natural frequencies of vibration that are usually damped (kept from getting large) by internal friction. If an object gets energy at a periodic rate matching a natural frequencies, the Amplitude of vibration can get VERY LARGE. This is called Resonance. Resonant Frequency is another name for natural frequency. Sources of Sounds All sounds have vibrations as their source!! Many forces (blows with a hammer, scraping with a bow, etc.) contain a range of frequencies. Only those frequencies matching the object's natural frequencies resonate. The same is true of air blown into an pipe. EA Lec Notes (Scen 101) Til6Ed-Chap Printed 03/30/2006, 1:18 PM

15 " Vibrating Strings Natural Frequencies of a Stretched String: Excite a stretched string near one end. Wave energy travels to the ends and is reflected back and forth. String vibrates at integer multiples of its lowest (fundamental) frequency. Interference causes some portions to move a lot, others not at all. See Fig.5.22,p.131. The points that do not vibrate are called nodes. The two fixed ENDS MUST BE NODES.!!!! The point(s) that vibrate most are called antinodes. Each Antinode Length = 1/2 wavelength. 1, 2, 3,... "nv 2 L, n String Natural Frequencies: f n n=1 is called fundamental frequency, others are overtones. Fundamental fixes each strings Pitch. Combined Overtones fix instument's characteristic quality. EA Lec Notes (Scen 101) Til6Ed-Chap Printed 03/30/2006, 1:18 PM

16 (Extra) Designing String Instrument s Fundamental Frequency: Formula for wave speed in string Fundamental Frequency X v #Tension Linear Density. X f 1 $1 2 L Tension Linear Density. Standing Waves: See Fig.5.21,p.131. (Not really standing, they just look that way) (DEMO) Resonance feeds in energy so that antinodes form on string. The situation is often called a "Standing Wave", but remember that there really are waves traveling out and reflecting back. Vibrating Air Columns Wind instruments (and organ pipes) also have natural frequencies. The Physics is different from strings: It's AIR that vibrates, so the speed, v = vsound = 343 m/s (at 20 C). Thus the wave speed is not available for tuning. Length of air column (like string length) determines frequencies. EA Lec Notes (Scen 101) Til6Ed-Chap Printed 03/30/2006, 1:18 PM

17 Sounds from Moving Sources Doppler Effect: occurs with all types of waves. Fig.5.24, p.132. Relative motion between observer and wave source changes the detected (Heard, seen, or measured) frequency. shorter). %% %% approaching each other, frequency is higher ( longer). %% %% moving away from each other, frequency is lower ( Doppler Effect Uses: Radar: Measured frequency shifts of reflected radio waves is accurate enough to determine speeds to less than one mph. Astronomy: Light from distant stars is shifted towards lower frequency (moving away). The shift increases with distance. This is strong evidence that the universe is expanding. Shock Wave: ( Draw Demo ) Fig.5.25, p.134. If the source is moving AT the speed of sound, the compression crests stay with the source and add up to a very large disturbance creating a Sonic Boom that moves with the source.. EA Lec Notes (Scen 101) Til6Ed-Chap Printed 03/30/2006, 1:18 PM

Producing a Sound Wave. Chapter 14. Using a Tuning Fork to Produce a Sound Wave. Using a Tuning Fork, cont.

Producing a Sound Wave. Chapter 14. Using a Tuning Fork to Produce a Sound Wave. Using a Tuning Fork, cont. Producing a Sound Wave Chapter 14 Sound Sound waves are longitudinal waves traveling through a medium A tuning fork can be used as an example of producing a sound wave Using a Tuning Fork to Produce a