LAB 203

THE SCIENCE

ACOUSTICS

INSTRUCTOR:

Dr. MAHMOUD KHALILI

TEXT BOOK:

Physics and Music

(The Science of Musical sound)

By:

H. White and D. White

Method of Evaluation

1: Project 10 Point

2: Homework 50 Point

3: Lab Report 60 Point

4: Quizzes 20 Point

Grade 5: Midterm Exam 100 Point

6: Final Exam 100 Point

7: Attendance 10 Point (Bonus)

Total 350 Point

Final Letter Grade:

Point Grade

300 - 350 A

255 - 299 B

205 - 254 C

170 - 204 D

0 - 169 F

1: Introduction

2: Biography of Person

Project 3: Scientific Contribution

(Any Discovery, Invention, Development.)

4: Conclusion

5: Reference

System of Measurement

Quantity SI^* C g S British

System

Length ( L ) meter ( m ) centimeter (cm) foot ( ft )

Mass( M ) Kilogram(Kg) gram ( gr ) slug

time ( t ) second second second

Weight ( W ) Newton ( N ) dyn pound (Ib)

Area ( A ) square square square

meter( m² ) centimeter(cm²) feet(ft²)

Volume( V ) cubic meter cubic centimeter cubic feet

(m³ ) (cm³ ) (ft³ )

Speed( v ) ( m / s ) ( cm / s ) ( ft / s )

Acceleration ( m / s² ) ( cm / s² ) ( ft / s² )

(a)

Force( F ) Newton(N) dyn pound(Ib)

SI^* : System International( Metric System)

Conversion Factors:

1 m = 100 cm 1 mile = 1.609 Km

1 m = 3.28 ft 1 mile = 5280 ft

1 Km = 1000 m 1 ft = 0.3.5 m

1 Kg = 1000 gr 1 Ib = 0.455 Kg

1 Kg = 2.2 Ib 1 Ib = 455 gr

1 A⁰ = 10^-10 m 1 ft = 12 inch

(Angstrom)

1 ( nm ) = 10^-9 m 1 inch = 2.54 cm

(nanometer)

1 µm = 10^-6 m

(micron)

SCIENTIFIC NOTATION:

0.1 = 1 x 10^-11 = 1 x 10⁰

0.01 = 1 x 10^-2 10 = 1 x 10¹

0.001 = 1 x 10^-3 100 = 1 x 10²

0.0001 = 1 x 10^-4 1,000 = 1 x 10³

0.00001 = 1 x 10^-5 10,000 = 1 x 10⁴

0.000001 = 1 x 10^-6 1,000,000 = 1 x 10⁶

(million)

1,000,000,000 = 1 x 10⁹

(billion)

0.00000936815 = 9.37 x 10^-6

1000,000,000,000 = 1 x 10¹²

(trillion)

0.0231 = 2.31 6400 = 6.40 x 10³

0.0067 = 6.7 x 10^-3 2453700 = 2.45 x 10⁶

SPEED OF LIGHT : 300,000 kilometers per second

( 186,000 miles per second)

SCIENTIFIC METHOD

I: Observation of the problem

II: Data and information

III: Theory

IV: Test and experiment

V: Scientific law

Theory(hypothesis) : A satisfying explanation of a

natural phenomenon.

Distance Traveled d

Speed (Velocity) = V =

Elapsed Time t

Note : If we specify the direction in which a body is moving, we refer to its motion as a Velocity, and without direction we refer as Speed. Both are in the same unit.

ACCELERATION: The rate of change of speed is

called acceleration.

V₂ - V₁

a =

t₂ - t₁

NEWTON'S LAWS OF MOTION:

(CLASSICAL MECHANIC):

1: Every body continues in a state of uniform motion in a straight line unless it is compelled to change that state by a force acting on it.

S F = 0 Þ a = 0

( a straight line motion with constant velocity)

d = v t

F : Force d: Distance

V: Velocity t: time

2: When a force acts on a body of mass m, it produces in it an acceleration equal to the force divided by the mass.

F = m a or m = F / a

3: To every action, there is an equal and opposite reaction.

THE LAW of UNIVERSAL GRAVITATION.

(NEWTON'S LAW of GRAVITY)

m₂ x m₁

F_g = G ------------

R²

m₂

m₁

O₁ F₁₂ F₂₁ O₂

G: 6.67 x 10^-11 ( m³ /Kg . s² ) Gravitational Constant

Newton's Constant

Weight = mass x acceleration due to gravity

F_g (W) = m g

work = Force x distance

w = F d

Energy: The ability to do work.

KE = 1/2 m v² PE = m g h

ME = KE + PE

KE = Kinetic Energy

PE = Potential Energy

ME = Mechanical Energy

m = mass of the object

v = Velocity of the Object

VIBRATING SYSTEMS

a a

Simple Pendulum Spring

0 0

a a a a

Common Characteristic of Vibrating Systems:

1: A center point. ( Equilibrium Point).

The point of rest. ( 0 )

2: Forces always point towards the center point.

3: Continuos Energy Conversion ( KE Û PE)

4: At any moment total energy of system is constant.

5: Amplitude ( a ) = Maximum or minimum displace-ment from equilibrium

4: Period ( T )= The time for one full vibration

(oscillation). The unit of period is Second (S )

5: Frequency (f) = The number of full vibration

( oscillation or cycles) in one second. The unit of frequency is Cycle per second (Cycle/S) or Hertz (Hz)

T = 1/f or f = 1/T

Hook’s Law : The applied force is proportional to displacement from equilibrium

F = K X

F: Applied force K = Constant number

X = Distance from equilibrium

Simple Harmonic Motion (SHM): The vibrating system which obey the Hook’s law defined as SHM. Such as simple pendulum, a spring pendulum, a vibrating strip, a tuning fork.

Damped Simple Harmonic Motion: Due to a resistance force the amplitude of vibration diminishes (decreases) gradually, until it finally comes to the rest . Period of the vibration remains the same .

Decay half time ( t ): It is the time required the amplitude of a Damped Simple Harmonic Motion to decreases to half.

t remains the same through the vibration and independent of amplitude.

a a a

Simple Harmonic Motion (SHM)

a/2 a/4

t t t a/8

time

Damped Simple Harmonic Motion

WAVES

a l

time (s)

WAVELENGTH ( l ): The distance between two similar point of the wave which they have the same wave character. The unit of wavelength is meter ( m )

WAVE PERIOD ( P ): The time required for wave to complete one full cycle is called period. The unit of period is second ( s )

WAVE FREQUENCY ( f ): The number of full cycle in one second is called frequency. The unit of frequency is Hz (cycle/s )

AMPLITUDE: The maximum deviation of a wave above or below the zero point

RELATION BETWEEN WAVES CHARACTERISTICS

FREQUENCY = 1 / PERIOD f = 1 / T

or or

PERIOD = 1 / FREQUENCY T = 1 / T

WAVE VELOCITY

WAVELENGTH =

FREQUENCY

l =

1: Transverse Waves

Method of propagation of waves

( Classification of waves ) 2: Longitudinal Waves

1: Transverse Wave: Waves whose vibration are perpendicular to the direction of propagation . (Surface water wave, waves on string )

Vibration

Propagation

2: Longitudinal Wave: Waves whose vibration are parallel to the direction of propagation . (waves on spring, sound wave)

0 Vibration

a a

Propagation

Note: Earthquakes produce both Transverse Waves and Longitudinal Waves.

PROPERTIES oF WAVE

1: Reflection 2: Refraction :

3: Diffraction 4: Interference:

5: Phase

Incoming Reflected

wave Normal wave

Q Q^/

2: Refraction:

Incoming Reflected

wave Normal wave

2: Refraction :

Q^/

Reflected

wave

3: Diffraction: The spreading of waves when it goes through a narrow opening or hits the end of a sharp obstruction.

Hole Screen Hole Screen

A A^’ A

B B^’ B

4: Interference: Combination of two waves whose amplitude added algebraically at any moment, is called the interference of two waves.

I : Constructive Interference

Interference II : Destructive Interference

C = A + B

B B

A C

In Phase Out of phase by 180⁰

(Constructive Interference) (Destructive Interference)

LIGHT: Light is a particular type of radiation and travels through space in the form of a wave with speed of C = 3 x 10⁸ m/s in vacuum (186,000 miles/s)

COMPONENT OF VISIBLE LIGHT: The small part of electromagnetic spectrum between 4000 A^o and 7000 A^o is visible light, which consists of Red, Orange Yellow, Green, Blue, and Violet. ( Fig. 2.7 )

Infrared Red Orange Yellow Green Blue Violet Ultraviolet

7000 A⁰ 4000 A⁰

FIGURE 2.7 Spectrum of visible light.

THE ELECTROMAGNETIC SPECTRUM

f(Hz) 10³ 10⁵ 10⁷ 10⁹ 10¹¹ 10¹³ 10¹⁵ 10¹⁷ 10¹⁹ 10²¹

Radio frequency V X Gamma

FM(88-108 MHz) Infrared I UV Ray Ray

AM(540-1650 KHz) s

l(cm) 10⁶ 10⁴ 10² 1 10^-2 10^-4 10^-6 10^-8 10^-10

FIGURE 2.8 Spectrum of electromagnetic radiation

SOUND

Sound is a longitudinal waves, needs a medium for its propagation( travel through). Speed of sound through fluid ( Fluid means Liquid or gas) increases with temperature. Speed of sound through different media increases with increase of rigidity of media. ( Rigidity is force between molecules of media)

SPEED oF SOUND IN AIR

V = 331 + 0.6T

V: Speed of sound( m/s )

T: Temperature in degree Celsius ( ⁰ C )

Temperature and Its Units: A measure of the amount of heat in an object, and an indication of the speed of the particles that comprise it. The unit for temperature are:

1: Fahrenheit(F) 2: Celsius (C)

3: Kelvin (K) or Degree Absolute