Nature of Sound, Signals, & Sine Waves

Question 1

What is a signal?

Answer 1

• A gesture, sound, or action that conveys information about how one parameter varies with another parameter
• Carries meaning
• EX: sound wave

Question 2

What is a system?

Answer 2

-Any process that produces an output signal in response to an input signal

Question 3

What is sound?

Answer 3

• Emphasize the physical not psychological perspective
• Sound source must be able to vibrate
  
  • Must have mass (m) and elasticity (E)
  • Medium of transmission must be capable of vibration
• Vibratory motion is caused by the interaction between inertia and elasticity –> to and fro movement
  
  • Consistent with Newton’s 3rd Law of Motion

Question 4

What is Newton’s 1st Law of Motion?

Answer 4

• Law of Inertia
• Any body in motion will stay in motion and any body at rest will stay at rest unless acted upon by another force
• Magnitude of inertia is proportional to mass

Question 5

What is Newton’s 3rd Law of Motion?

Answer 5

• Law of Restoring Forces
• With every force there is an equal and opposite reaction force
• Vibration: elasticity is the reaction to inertia
• Vibration continues without reapplication of external force and is sustained by the opposing forces

Question 6

Describe the vibratory motion of a spring.

Answer 6

• System engages in simple harmonic (sinusoidal) motion
• Spring can be compressed
  
  • Elasticity (restoring forces) opposes deformation forces
• As the spring is compressed, greater force is required for additional compression

Question 7

What is Hooke’s Law?

Answer 7

• Magnitude of restoring force (F) is directly proportional to the magnitude of displacement (x)
  - -> F = -k * x
  - Stiffness is the spring constant “k”
  - Compliance is the inverse of stiffness

Question 8

Describe the movement of the pendulum.

Answer 8

• Example of slow moving vibration
• Restoring force is gravity not elasticity
  - Gravity is highest at peak heights (max. potential energy)
  - Elasticity is highest at equilibrium (max. kinetic energy)
• Period of pendulum: T = 2 * pi * sqrt(L/G)

Question 9

Describe the movement of the tuning fork.

Answer 9

• Example of movement of air mass
• Alternate regions of compressions/rarefactions
  - Density increases: compression
  - Density decreases: rarefaction
• Medium isn’t displaced over a great distance (disturbance wave moves through elastic medium)
• Sound propagation of density changes through an elastic medium
• Sound source acting on a medium
  - Place the tuning fork in the medium
  - Before force, particles are equidistant from each other
  - Particles move about positions of equilibrium because of m and E

Question 10

Describe types of wave motion.

Answer 10

-Classified by direction of vibration of medium re: direction of wave propagation

• Transverse Wave Motion
  - Vibration is perpendicular to direction of wave propagation
  - Elements move up and down (note peaks and valleys)
• Longitundinal Wave Motion
  - Direction of particle movement is parallel to wave movement
  - Elements of move back and forth (note nodes and antinodes)
  - Sound waves are longitudinal waves

Question 11

Describe the properties of the transmitting medium.

Answer 11

-Mass (m)

• Elasticity (E)
  - Property that enables recovery from duration of shape/volume
• Density (rho)
  - Mass per unit of volume
  - Decreases as you rise above sea level
• Atmospheric Pressure
  - 14.7 lb/in^2
  - 100,000 N/m^2
  - 1,000,000 Pa

Question 12

List the characteristics of sound.

Answer 12

• Frequency (f)
• Amplitude (A)
• Phase (phi)
• Wavelength (lamda)
• Speed (v)

Question 13

What is frequency?

Answer 13

• Cycles per second (Hz)
• Inverse of period
• Determined by source characteristics
• Correlates to perceived pitch

Question 14

What is amplitude?

Answer 14

• Correlates to perceived loudness
• Instantaneous vs. average amplitude
• Root Mean Square (RMS) Amplitude

Question 15

What is phase?

Answer 15

• When a sine wave starts at some arbitrary time (time shifts)
• Measured in degrees or radians
• Little effect on perception

Question 16

What is the speed of sound?

Answer 16

• Governed by properties of medium
• Speed of sound = 331 m/s at sea level/0 degrees C
• -> V = sqrt(E/rho)
• -> V = 331 + .62 * Tc

Question 17

What is wavelength?

Answer 17

• Distance between 2 peaks or 2 troughs

- -> V = lamda * f

Question 18

What is the formula of a sine wave?

Answer 18

x(t) = A * sin(2 * pi * f * t + phi)

Question 19

What makes vibration stop?

Answer 19

• Frictional resistance that opposes motion and limits velocity
• Kinetic energy transferred to thermal energy results in damping

Question 20

Describe transfer of energy.

Answer 20

• Sound is defined as a transfer of energy through an elastic medium
• Energy is transferred in the direction the sound is propagated
• Air mass offers resistance
• Kinetic energy is transferred to thermal energy