Dr / Horia Fawzy

Intensityof sound waves.

Intensity of sound: Is the sound energy passaging through a unit
area per unit time(W/m2)
𝑬 𝑷
𝐈= =
𝑨.𝒕 𝑨
Threshold of Hearing (I0) : Is the sound level which a persons ear
is unable to detect any sound(10-12W/m2) =(0dB).
Loudness = sound level (𝑳):Is a measure of the intensity of particular
sound to the intensity that it is heard at the threshold dB: decibel
.
𝐈
L=10Log ( 𝐈𝟎
) L=10Log 𝐈-10 Log 10−12

L=10(Log 𝐈-log I0)

L=10Log 𝐈 +120
A quiet library has sound intensity of 1x10-8 W/m2, calculate the
sound level?

 Answer:
Loudness = sound level (𝑳) 𝑰0=𝟏𝟎−𝟏𝟐 w/m2

𝐈
L=10Log ( 𝐈𝟎
)

L =10Log (𝟏𝟎−𝟖 /𝟏𝟎−𝟏𝟐 )

L = 40 dB
 Types of waves
2- Electromagnetic Waves(EM)
It is not necessary to have a medium for the electromagnetic
waves in order to propagate in it. i.e. can propagate in vacuum.

 Characteristics of Electromagnetic waves.

(1) It consists of an electric field component and a

magnetic field component which are perpendicular to
each others.

(2) It propagate with constant speed in a direction perpendicular

to both the electric and magnetic field components
(3x108m/sec) .

(3) It can propagate even in the absence of any medium.

2- Electromagnetic Waves(EM)
 Characteristics of Electromagnetic waves.

(4) It transvers waves and can polarized.

(5) Don’t affected by electric field and magnetic field because it

non charged

(6) It can reflected ,refracted ,interference ,diffracted

Introduction
Solar radiation interaction with the earth’s atmosphere:

1. Reflected back Radiation

2. Absorbed Radiation Reflected

3. Scattered Radiation scattering

4. Direct incident Radiation

5. Diffused Radiation

Absorbed

The light reaching the life- Diffuse

direct
bearing region on the
earth’s surface finally
is either direct or diffused.
Electromagnetic Waves (EM)
 Visible Light(V.B)
(λ=400-700nm).
*Shorter Wavelength than Infrared Light
*Higher Frequency than Infrared Light
*Higher Energy than Infrared Light
Examples that reflect visible light:
Sun, Light Bulbs, Red
Visible Light is the only part of the EM
Orange
spectrum that the human eye can see. Yellow
Red light= longest wavelength; lowest Green
frequency
Violet light= shortest wavelength; higher Blue
frequency Indigo
White light= all colors mixed together
Violet
 What is light ?

Light is electromagnetic radiation of a specific

wavelength(400-700nm) and frequency that is detectable by
the human eye.
Light is usually considered to be the visible part of the
spectrum.
 Conclusion(light theory)

Newton (1643) Huygens (1690) Maxwell (1862) Einstein (1905)


c  E  mc 2 h

 E  h  h mc

Radio Waves(RF)
(λ=10cmto100m).

*Longest Wavelength
*Lowest Frequency
*Lowest Energy
Examples-TV signals,
communicate to send
signals to the antennas
on the earth (satellite)&
FM radio signals
Radio waves travel easily
through the atmosphere
and many materials.
 Microwaves(MW)
(λ=10cmto100m).
*Shorter Wavelength than Radio
Waves
*Higher Frequency than Radio
Waves
*Higher Energy than Radio
Waves
Examples-Cell Phones and Radar
Microwave ovens produce
microwaves that cause water
molecules in food to vibrate
faster, which makes food
warmer .
 Infrared Waves(IR)
(λ=700nm to 1mm).
*Shorter Wavelengths than Microwaves
*Higher Frequency than Microwaves
*Higher Energy than Microwaves
Examples- Sun, Fire and Radiator
All objects emit infrared waves-usually
given off by hot objects (stars, lamps,
people and animals).
Infrared radiation is the type of EM wave
most often associated with heat.
 Ultraviolet Light(UV)
(λ=100nmto400nm).
*Shorter Wavelength than
Visible Light
*Higher Frequency than Visible
Light
*Higher Energy than Visible Light
Examples-Sun and special lamps
(tanning bed)
The wave can damage your skin and eyes.
Uses: Sterilize medical equipment, help the
produce vitamin D, harden dental fillings,
and tanning.
 X-Rays
λ=(1nm to100nm).
Shorter Wavelength than
*

Ultraviolet Light
*Higher Frequency than
Ultraviolet Light
*Higher Energy than Ultraviolet
Light
Examples- X-ray machines to
view bones and airport
security
X-rays have enough energy to go
through skin and muscle but
are absorbed by the bone.
Can be dangerous for a living
organism.
 Gamma Rays(𝜸-Ray)
(λ=1nm to 0.01nm).
*Shortest Wavelength
*Highest Frequency
*Highest Energy
Examples- Sun, other stars and
radioactive substances
Used to kill cancer cells and fight
tumors.
Can be dangerous for a living
organism.
How are Mechanical and EM waves similar and
different?
Mechanical Waves
EM Waves
Reflect, absorb,
refract, diffract Travel as
Travel through
longitudinal/
A vacuum
Carry energy compression
waves

Travel at the Have amplitude,

same speed= wavelength, frequency Travel in a
3x108m/sec medium
Travel as
Transverse waves
Have many Travel at different
valuable uses Many different speeds
wavelengths
1. Sound Wave Ocean Wave Wave on a rope Stadium Wave

Which one does not belong? Why? ______________________________________________________

__________________________________________________________________________________

2. Microwave X-ray Laser Sound Wave

Which one does not belong? Why? ______________________________________________________

__________________________________________________________________________________

3. Radiation Radio Signal Light Earthquake

Which one does not belong? Why? ______________________________________________________

__________________________________________________________________________________

4. Sound Wave Ripple in water Guitar String TV Signal

Which one does not belong? Why? ______________________________________________________

 Waves can also be classified according to the number of dimensions in which
they propagate energy to:

● One dimensional waves : Waves moving along the string or the spring

●Two dimensional waves: Surface waves or ripples on water, caused by

dropping a pebble on a quit bond.

● Three dimensional waves : waves that emitted

radially from a small source(isotropic source) .
 Traveling Waves

● Any one-dimensional wave traveling with a speed (v) in the x direction

can be represented by a wave function of the form:

y(x,t) = f (x ± vt)
The negative sign applies to a wave traveling in the positive x direction
The positive sign applies to a wave traveling in the negative x direction
General Linear wave equation
T sinθB
An element of astringe under tension T

T sinθA

For small angleθ so sinθ=tanθ

Linear wave equation
𝝏𝒚 𝒚
Tanθ= θ
𝝏𝒙 μ 𝜕2𝑦
𝒙
2 =
𝑻 𝜕𝑡 ∆𝒙

From newton's second law

𝑻
𝐹𝒚 = ∆𝑚𝑎𝑦 ν=
μ
Linear mass density
μ=
∆𝒎 1 𝜕2𝑦 𝜕2𝑦
∆𝒙 2=
𝜕2𝑦 𝒗𝟐 𝜕𝑡 𝜕𝑥2
𝐹𝒚 = μ∆𝒙𝑎𝑦=μ∆𝒙 𝜕𝑡2

𝜕2𝑦
𝐹𝒚 = μ ∆𝒙 =
𝜕𝑡2
 General Expression of Sinusoidal Wave

●Consider the sinusoidal wave in Figure , which shows the

position of the wave at t =0
●Because the wave is sinusoidal, we expect the wave
function at this instant to be expressed as
y(x, 0) = A sin aX (i)

Where (A) is the amplitude

a is a constant to be determined

at X = 0, we see that y(0, 0) = A sin a(0) = 0, consistent with Figure

The next value of X for which y is

zero is X =λ/2. Thus
For this to be true, we must have
 General Expression of Sinusoidal Wave

𝒀(𝒙, 𝒕) = 𝑨𝒔𝒊𝒏(𝒌𝒙 − 𝝎𝒕)

Here we assume that the vertical position y
of an element of the medium is zero at x = 0
and t =0. This need not be the case. If it is not

The general expression for sinusoidal wave is:

𝒀(𝒙, 𝒕) = 𝑨𝒔𝒊𝒏(𝒌𝒙 − 𝝎𝒕 + 𝝋)

A :is the amplitude

𝟐𝝅
K: is the angular wavenumber = Rad/meter
𝝀
𝟐𝝅
ω: is the angular frequency= 2πƒ=
𝝉
𝝋: is the phase constant
 Example(1)
A sinusoidal wave is described by Y = (0.25 m) sin(0.30x - 40t) where x and y
are in meters and t is in seconds. Determine for this wave the (a) amplitude,
(b) angular frequency, (c) angular wave number, (d) wavelength, (e) wave
speed, and (f) direction of motion.
Answer (d) wavelength,
𝟐𝝅 𝟐𝝅
𝝀= = =20.9m
𝑲 𝟎.𝟑
Y = (0.25 m) sin(0.30x - 40t)
𝝎
(e) wave speed v=
𝒀(𝒙, 𝒕) = 𝑨𝒔𝒊𝒏(𝒌𝒙 − 𝝎𝒕) 𝑲
𝟒𝟎
= =133 m/s
𝟎.𝟑
(a) amplitude, 𝑨 = 𝟎. 𝟐𝟓𝒎
(f) direction of motion. to
𝒃 angular frequency,𝝎=40 rad/s
the right( + x direction)]

𝒄 angular wave number 𝒌=0.3 rad/m

The Speed of Waves on a Stretched Strings

●The speed of a wave traveling on a

stretched string of mass per unit length
μ and tension T is given by:

𝑻 𝒎 𝒎a𝒔𝒔
ν= 𝝁= =
𝝁 𝑳 𝑳𝒆𝒏𝒈𝒉𝒕

V :is the wave speed

●The wave speed v increases with increasing tension T. and the

wave speed should decreases as the mass per unit length μ of the
string increases.