Hearing Science (Washnik)

8/25 & 9/8

Oscillation

-A motion in which an object shows regular fluctuation in value, position, and/or state about a mean value

In Oscillation, there is no…

irregular movement

Oscillation is like a…

Pendelum (# of cycles per second)

Oscillations increase when what increases?

Speed

Draw the properties of a sine wave

*Answers in powerpoint because they won’t let me add a picture

Phases are always in…

Degrees

What are the 2 ways to measure amplitude

1. Peak to peak (+ peak to - peak)

2. Baseline/reference line to peak amplitude

Frequency (f)

Number of cycles per second

What unit is frequency in?

Hertz (Hz)

Period (T)

Amount of time required to complete one cycle

What unit is period in

Seconds (s)

Inverse Relationship

C=1/D

C increases → D decreases

C decreases → D increases

Direct Relationship

A=B

A increases → B increases

A decreases → B decreases

What is the relationship between f and T

Inverse

f=1/T

T=1/f

An object in simple harmonic motion completes 3000 oscillations in a second. Calculate its frequency.

3000Hz

Wavelength

-The distance from one peak/trough of the wave to the next adjacent peak/trough

-2 consecutive identical points

What unit is wavelength in?

Meter

High frequency has…

Peaks closer together making shorter wavelengths

Low frequency has…

Peaks farther apart making longer wavelengths

Physical Perception of Frequency

100 Hz, 1000Hz, 8000Hz

Psychological Perception of Pitch

No sound, low, medium, high

Is there a relationship between frequency and pitch of a sound wave?

Yes! Frequency is related with pitch of a sound

Mechanical Waves requires…

A medium to propagate

Mechanical waves are disturbances traveling in a what?

Elastic medium (like air, glass, metal, etc)

Transverse Waves

Particles of the medium move in perpendicular to the direction in which the wave travels (string waves)

Longitudinal Waves

Particles of the medium move parallel to the direction in which the wave travels

100 Hz sine wave has _____ wave length than 1000 Hz sine wave

Longer

Shorter

Equal

Longer

What kind of relationship do wavelength and time have?

Direct

F↑ → T↓ → λ↓

What kind of relationship do wavelength and frequency have?

Indirect

F↓ → T↑ →λ↑

What is the frequency of a sine wave with 10 sec. period?

0.1 Hz

1 Hz

10 Hz

100 Hz

0.1 Hz

What are the 3 prerequisites for production of sound

1. A medium of transmission

2. A source of energy

3. A vibrating object that generates audible pressure

What are the 3 important properties of any medium

Mass, Density, and Elasticity

What is the best and fastest medium and why?

Solid because the molecules are closer together and can hit each other faster

What is mass

Amount of matter that is present

Is there a difference between mass and weight?

Yes! Weight takes gravity into account, mass does not

Density is…

The amount of mass per unit volume

Elasticity

Application of force on solid, liquid, or gas → distortion of either shape or volume or both

Is a thicker or thinner wire more elastic and why?

Thicker wire is more elastic because it has a higher elastic limit and needs more force to be squished

Hooke’s Law

The magnitude of restoring force of elasticity is directly proportional to the magnitude of spring displacement

What is the formula for Hooke’s Law

Fr=-kx

Fr= restoring force of elasticity

x= magnitude of displacement of the spring

K=spring constant

Stiffness explains why springs require…

Greater force than others to be compressed or extended

Stiffer spring →

More force needed to squish

Compliance and stiffness have a ____ relationship

Inverse

Newton’s 1st Law

All bodies remain at rest or in a state of uniform motion unless another force acts in opposition

Newton’s 3rd Law

For every action, there is an equal and opposite reaction

MKS System

Meter, kilogram, and second system (most used)

CGS System

Centimeter, gram, second system

Displacement

Changes in position

Distance

Changes in position with direction AND distance

Scalar Quantities

Mass, time, and energy, only described by reference to magnitude

Velocity is a _____ quantity

Vector (has magnitude and direction)

Acceleration(a)

△c/time (△c=change in velocity)

If a train travels at a velocity of 20 m/sec and then is accelerated to a velocity of 50m/sec, and if this change is accomplished in 6 seconds then acceleration is what?

5 m/sec²

Newton’s 2nd Law

The acceleration of an object is directly proportional to the next force applied to the object and inversely proportional to the mass of the object (F=ma)

Pressure

Amount of force per unit area (p=F/A)

Momentum=

Mass x velocity

Kinetic Energy

-A form of energy that results from an object in motion

-Types of motion → translation, rotation, vibration

-K.E. (1/2)mv²

Potential Energy

-Form of energy that results from object position or arrangement of parts. STORED ENERGY

-P.E.= mgh

-m=mass, g=gravity, h=height

Work

-When force succeeds in moving a body that the force acts upon, and the quantity of work is given by the product of magnitude
-W=Fd (F=force, d=displacement

Speed of Sound in air is given by…

s=√E/p

E=elasticity, p=density

What does speed of sound not affect?

Frequency & intensity

Complex Sound

More than 1 frequency component

Periodic Sound

Repeating sound

Fundamental Frequency

-The lowest frequency (f₀)

Harmonics

-Higher frequency components

-Integer multiples of f₀

Time Domain for Periodic Sounds

-Repeating pattern of pressure change

-Within the cycle, things looks complex

Frequency Domain for Periodic Sounds

-Spectral peaks at evenly spaced frequency intervals

-”picket fence” appearance

Complex Wave

-Any sound wave that is not sinusoidal

-Consists of a series of simple sinusoids that can differ in amplitude, frequency, and phase

-AKA Fourier Series

Fourier Analysis

Any complex wave can be decomposed to determine the amplitudes, frequencies, and phases, of the sinusodal components

Sawtooth Wave

-Complex periodic wave with energy at all harmonics (odd & even)

-Amplitude decreases as the inverse of harmonic number

Square wave

-Complex periodic wave where energy is only at odd multiples of f₀

-Spectral Envelope slope of -6dB/octave

-Amplitudes decrease as the inverse of the harmonic number

Octave

Doubling frequency (can go up or down)Tri

Triangular Wave

-A complex periodic wave with energy only at odd harmonics

-Slope of envelope is steeper for triangular wave

-Spectral Envelope Slope of -12dB/octave

Pulse Wave

-Complex periodic wave derived from the square wave

-The second part of the cycle is replaced by absolute silence

-Each pulse in the wave has some width or duration P_d

Pulse Repetition Frequency (PRF)

1/T

A pulse wave has harmonics at…

Odd and even integer multiples of the pulse repetition frequency

What does the amplitude spectrum show for pulse waves?

Lobes and valleys (nulls)

-Nulls occur at integer multiples of reciprocal of P_d

Aperiodic Sounds

Do not repeat themselves

What do aperiodic sounds not have?

Fundamental frequency (can have lower though)

Time Domain for Aperiodic Sounds

No repeating patter of pressure change

Frequency Domain for Aperiodic Sounds

-The spectrum is dense

-No “picket fence”

-Auditory impression sounds noisy

Reflection

When a sound wave encounters obstacles in the mechanical medium, it changes its traveling path

Refraction

Bending of sound waves when they enter in a different medium with any angle except 90 degrees

Diffraction

Involves a change in direction of waves as they pass through as opening or around a barrier in their path

What is Interference?

-A condition in which two or more waves carrying energy meets up and overlap

-The energy carried by them get mixed up during interference

Constructive Interference

Amplitude of the final wave will be larger compare to the original waves

-Add together

-Must have same amplitude, phase, and frequency

Destructive Amplitude

Amplitude of the final wave will be smaller than the original waves

-Same frequencies and amplitudes

-Different phases

String Waves

Can be produced by stretching a string

Standing/Stationary Waves

Results of interference between two waves traveling in opposite directions

Harmonics/Partial

A component frequency of the output signal that is an integer multiple of the f₀

The 1st harmonic is known as what?

The fundamental frequency (f₀)

The 2nd harmonic is known as what?

The 1st overtone

Beat

An interference between two sounds of slightly different frequencies

What are beats perceived as?

Periodic variations in volume whose rate is the difference between the two frequencies

Combining a 250 Hz tone with a 253 Hz tone results in how many beats per second?

3

What is the 5th harmonic of 1000Hz?

500

50

50,000

5000

5000

Two sine waves propagating in opposite directions will result in a ______

Standing wave

Reflection will be best if there is a ___

Hard barrier

Loose barrier

Soft barrier

No barrier

Hard barrier