Waves and Sound Guided Notes

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Waves and Sound Guided Notes

Section 1: Intro to Waves

•  Waves

–  Are disturbances that move through an empty space or through medium (material)

–  Waves transfer energy without transferring matter.

–  Particles of medium move in simple harmonic motion

•  Two Major Classes of Waves
–  Mechanical wave:
•  Caused by a disturbed medium and move by action reaction of particles
•  A medium is matter particles like gas (ex. air), liquid (ex. Water), and solid (ex. earth)
–  Electromagnetic wave:
•  Move through empty space (no medium)
•  Created by moving electrons
•  Ex. radio waves, microwaves, light
–  In order to start and transmit a wave, a source of disturbance (vibration) and a disturbed medium are required.
•  Mechanical caused by vibrating particles
•  Electromagnetic by vibrating electrons
–  wave pulse is a single wave disturbance
–  wave train (continuous wave) - is a series of pulses at intervals
•  Damping:
–  A decrease in the amplitude of a wave
–  Caused by energy loss or the spreading out of the wave over a larger area. /
Mechanical Wave

Electromagnetic Wave
Section 2: Types of Mechanical Waves
•  Transverse Wave:
–  Wave particles move perpendicular to the direction the wave travels
–  Ex. vibrating string of a musical instrument
–  Parts of a Transverse Wave:
•  crest- highest point on a transverse wave
•  trough- lowest point on a transverse wave
•  equilibrium position- center around which simple harmonic motion occurs
•  amplitude- from the equilibrium position to the crest or trough
•  Longitudinal Wave:
–  Particles vibrate parallel to the direction the wave travels
–  ex. sound wave
–  Parts:
•  compression- point where the particles are closest together
•  rarefaction- point where the particles are furthest apart /
Section 3: Relationship between Wavelength, Frequency and Wave Speed
•  velocity (v) - speed of the wave.
–  unit: m/s (meter/second)
•  frequency ( f ) - vibrations per second of the wave
–  unit: Hz (hertz)
•  wavelength (λ) - length of one wave pulse
–  unit: m (meter)
– 
•  Relationship between frequency and wavelength.
–  Wavelength and frequency are inversely related
–  As frequency goes up the wavelength gets shorter (assuming no change in velocity)
•  Period (T) – seconds for one cycle (unit s)
•  Frequency (f) – cycles for one second (unit Hz) /

Example 1: The frequency of a wave is 560 Hz. What is its period?

Example 2: A girl floats in the ocean and watches 12 wave crests pass her in 46 s. Calculate the wave:

a) frequency b) period

Example 3: The period of a wave is 0.044s. How many cycles will the energy source make in 22s?

Example 4: A distance of 0.33 m separates a wave crest from the adjacent trough, and the vertical distance from the top of a crest to the bottom of a trough is 0.24m.

a) What is the wavelength? b) What is the amplitude?

Example 5: What is the speed of a 256 Hz sound with a wavelength of 1.35 m?

Example 6: You dip your finger into a pan of water 14 times in 11s, producing wave crests separated by 0.16 m.

a. What is the frequency? b. What is the period? c. What is the velocity?

Section 4: The Pendulum

•  Pendulum- a weight on a string that moves in simple harmonic motion (swings back and forth).
•  Movement from a to c and back to a is one complete cycle or vibration
•  Simple harmonic motion- vibration about an equilibrium position
•  Constant back and forth motion over the same path.
•  15º is the maximum angle for a pendulum to have simple harmonic motion where our equations work
•  Masses do not effect the period in a pendulum.
•  What effects the period:
•  L – length of the string
•  g – acceleration due to gravity /

Example 7: A tall tree sways back and forth in the breeze with a frequency of 2Hz. What is the period of this tree?

Example 8: Hypnotist Paulbar the great swings his watch from a 0.20 m chain in front of a subjects eyes. What is the period of swing of the watch.

Example 9: A spider swings slightly in the breeze from a silk thread that is 0.09 m in length. What is the period of the simple harmonic motion?

Example 10: If a pendulum is shortened, does the period increase or decrease? What about its frequency?

Section 5: Wave Interactions
Reflection:
•  The turning back of a wave at the boundary of a new medium
•  Ex: light off a mirror, or sound echo
•  Incident wave- incoming
•  Waves reflected off a fixed boundary are inverted.
•  A fixed boundary is one not allowed to move
•  Waves reflected off a flexible boundary are upright.
•  A flexible boundary is allowed to move
Law of Reflection:
•  Angle of reflection of a wave equals angle of incidence (θr = θi)
•  Normal line – line perpendicular to surface being reflected off of.
Example 11: Draw the reflected wave, labeling angles of incidence, reflection, and the normal line
/



Waves in Phase

Wave front:

•  Portion of a medium’s surface in which particles are in phase

•  Particles in phase are in the same stage of their vibration.

Example 11: Which two of these particles would be in phase?

Refraction:
•  the bending of a wave path as it enters a new medium obliquely (indirectly)
•  caused by difference in speed of the new medium
•  fast to slow – bends toward the normal line
•  slow to fast – bends away from normal
Example 13: Draw the refracted wave, labeling the normal line, angle of incidence, and angle of refraction.

Diffraction:
•  Spreading of waves around edges or through an opening of a boundary
•  Is greatest when size of opening is smaller than wavelength /
Diffraction: Bending around opening

Principle of Superposition:

•  Displacement of a medium by two or more waves is the algebraic sum of the displacements of the waves alone

Interference:

•  Result of the superposition of two or more waves

•  constructive- (crest meets crest or trough meets trough) amplitudes add

•  destructive – (crest meets trough) amplitudes subtract

•  Only temporary as paths cross

Example 14: Finish the drawings showing the type of interference

Interference with wave fronts creates these:
•  antinodal line
•  Lines of constructive interference
•  nodal line
•  Lines of destructive interference
Standing wave:
•  created by waves with same frequency, wavelength, and amplitude traveling in opposite directions and interfering.
•  consists of nodes (o amplitude) and antinodes (max amplitude)
•  produced by certain frequencies /

Section 6: Sound

•  Sound waves are produced by a vibrating object

•  Sound waves are longitudinal mechanical waves.

•  Sound Frequency determines pitch

•  20 – 20,000 Hz is audible sound (average human can hear)

•  Less than 20 Hz are infrasonic

•  Greater than 20,000 Hz are ultrasonic

•  Sound Velocity

•  Largely depends on medium elasticity

•  Solids>liquids>gasses

•  Then depends on temperature

•  Faster at higher temperatures

•  Air (at 0ºC) v = 331 m/s and +/- 0.6 m/s per ºC

Sound Velocity Equations

v = 331 + 0.6 Tc v = d/t v = fλ

Example 15: What is the speed of sound at room temperature (22ºC)

Example 16: How many seconds will it take to hear an echo if you yell toward a mountain 110 m away on a day when air temperature is -6.0 ºC?

Example 17: If sound travels at 340 m/s, how many seconds will it take thunder to travel 1609m?

Example 18: A sonar echo takes 3.1s to go to a submarine and back to the ship. If sound travels at 1400m/s in water, how far away is the submarine?

Example 19: On a day when air temperature is 11ºC, you use a whistle to call your dog. If the wavelength of the sound produced is 0.015m, what is the frequency? Could you hear the whistle?

Section 7: The Doppler Effect

•  The Doppler Effect
•  Change in pitch caused by relative motion of source and observer
•  Pitch increases as sound and observer approach
•  Pitch decreases as sound and observer move away
Equation

•  v is the speed of sound you can solve for it if given temperature or else just use 340 m/s in most problems
•  vs is the speed of the source and + if approaching the observer
•  vo is the speed of the observer and + if approaching the source /

Example 20: Sitting on a beach at Coney Island one afternoon, Sunny finds herself beneath the flight path of airplanes leaving Kennedy Airport. What frequency will Sunny hear as a jet, whose engines emit sound at a frequency of 1000 Hz, flies towards her at a speed of 100.0 m/s? (use 340 m/s as the speed of sound)

Example 21: Sitting on a beach at Coney Island one afternoon, Sunny finds herself beneath the flight path of airplanes leaving Kennedy Airport. What frequency will Sunny hear as a jet, whose engines emit sound at a frequency of 1000 Hz, flies away from her at a speed of 100.0 m/s? (use 340 m/s as the speed of sound)

Example 22: A sparrow chases a crow with a speed of 4.0 m/s, while chirping at a frequency of 850.0 Hz. What frequency of sound does the crow hear as he flies away from the sparrow at a speed of 3.0 m/s? (use 340 m/s as the speed of sound)

Section 8: Intensity and Perceived Sound

•  The property of sound waves associated with loudness is amplitude

•  The property associated with pitch is frequency

•  Sound intensity is the rate of transferring energy through an area

•  The Decibel Scale

•  Threshold of hearing (Io)- the minimum intensity sound that can be heard at certain frequencies

•  ß = 0 dB at the threshold of hearing

•  The decibel scale relates sound intensity to human hearing

•  An intensity of 0 dB is when there is enough energy for an average human to detect the sound

•  1-dB in intensity level is the smallest change in loudness that an average listener can detect

•  If the relative intensity level increases by 10 dB, the new sound seems approximately twice as loud as the original sound.

Section 9: Resonance and Music

•  Forced Vibration- The vibration of an object that is made to vibrate by another vibrating object.

•  Sympathetic vibrations- secondary vibrations caused by forced vibration of a first object.

•  Sounding board- part of an instrument forced into vibration to amplify sound

•  Resonance

•  Also called sympathetic vibrations

•  Dramatic increase in the amplitude of a wave when the frequency of an applied force matches the natural frequency of the object.

•  All objects have a natural frequency

Types of Instruments
•  Percussion Instrument
•  Musical sound produced by striking the object
•  Frequency depends on the mass of the object.
•  To raise the pitch- decrease the mass of the object.
•  Ex- drums, xylophone, bells
•  String Instrument
•  Musical sound produced by plucking or blowing strings
•  Frequency depends on four factors
•  To raise pitch
•  1. decrease diameter of string
•  2. increase tension
•  3 decrease length
•  4. decrease density of string material
•  Examples: guitar, violin
•  Wind Instrument
•  Musical sound produced by vibrating air column
•  Frequency depends mainly on length of air column
•  To raise pitch- decrease the size of the air column
•  Examples- oboe, flute / Open-Ended Wind Instrument

Closed-Ended Wind Instrument

Acoustics

•  Acoustics- field of study related to sound

•  Acoustic designers try to maximize the quality of sound reaching the audience

–  Control the size, shape, and material used

–  They try and control the reflection

•  Reverberation- If a reflected sound wave reaches the ear within 0.1 seconds of the initial sound, then it seems to the person that the sound is prolonged.

•  Echoes- A perceived second sound that arrives after the first has died out.

–  Echoes occur when a reflected sound wave reaches the ear more than 0.1 seconds after the original sound wave was heard.

•  Interference causes beats

–  Beats occur due to constructive and destructive interference between sounds with close but not exact frequencies.