Transcript Here

Tutorial 3
Wave
Q1. In Young's double slit experiment, if
we know that the distance from the
center line to the first bright fringe is
5cm, what is the distance from the third
to the fourth bright fringe?
• d sin θ = m λ
m = order of the bright fringe
d (y1/L) = λ
λ * L/d = y1 = 5 cm
• y4 – y3 = (4 λ – 3 λ) * L /d
=λ*L/d
y4 – y3 = 5 cm
So the distance from the third to the fourth bright
fringe is 5 cm
http://hypertextbook.com/physics/waves/introduction/
Additional notes
Interference – Young’s Double-Slit
Experiment
The interference occurs because each point on the
screen is not the same distance from both slits.
Depending on the path length difference, the wave can
interfere constructively (bright spot) or destructively
(dark spot).
Slit separation = d;
Distance on screen = x
Angle of incidence = θ
x
= mλ  bright
= (m + ½)λ  dark
m = 0, 1, 2, …
L
sinθ ~ tanθ ~ θ ~ x/L, small θ
Interference – Young’s Double-Slit
Experiment
We can use geometry to find the conditions for
constructive and destructive interference:
{Approx.: sinθ ~ tanθ ~ θ ~ x/L, small θ}
Q2. Why would it be so that our eyes
did not evolve such that we can see
deep ultra-violet light?
• It would damage our eyes because ultra-violet
light carries high energy
• Most organisms with colour vision are able to
detect ultraviolet light. This high energy light can
be damaging to receptor cells. With a few
exceptions (snakes, placental mammals), most
organisms avoid these effects by having
absorbent oil droplets around their cone cells.
• The alternative, developed by organisms that had
lost these oil droplets in the course of evolution,
is to make the lens impervious to UV light - this
precludes the possibility of any UV light being
detected, as it does not even reach the retina
Q3) A 60 Hz vibration produces waves
in air that propagate at 340 m/s. What
is the
Speed of the wave
Their frequency
The wavelength
The period
a) Speed: v = 340 m/s
b) Frequency: f = 60 Hz
c)
Wavelength:  
d) Period: T 
v
 5.67 m
f
1
 0.0167 s
f
Question 4
• Physics in movies:
– In some western movies one sees the
Red Indians scouts putting their ear to
the ground. Explain the physics reason
behind this action.
– In many science fiction movies,
explosions taking place in outer space
are seen and heard at the same time.
What errors in physics are there in
those scenes?
Material
v (m/s)
Gases
Hydrogen (0°C)
1286
Helium (0°C)
972
Air (20°C)
343
Air (0°C)
331
Liquids at 25°C
Glycerol
1904
Sea water
1533
Water
1493
Mercury
1450
Kerosene
1324
Methyl alcohol
1143
Carbon tetrachloride
926
Solids
Diamond
12000
Pyrex glass
5640
Iron
5130
Aluminum
5100
Brass
4700
Copper
3560
Gold
3240
Lucite
2680
Lead
1322
Rubber
1600
Q4. Sound Speed VS Medium
Sound needs medium to propagate. Hence, it’s impossible to hear any
sound in outer space. And it takes time for sound to propagate. Hence it’s
also impossible to hear and see the explosion at the same time ^_^
Sound wave
Q5
• Do sound waves bend towards or
away from the ground on hot day?
Explain why?
Q5. Sound Speed VS
Temperature
vsoundinair ~ T
Sound travel at higher temperature vsound( inair)  331.4  0.6Tc (m / s )
In daytime, the ground is warmer than the atmosphere. As a result, the sound
waveform travels at different speed (the waveform nearer to the ground
travels faster than the one farther from the ground), causing the overall
sound waveform to bend upward. It is exactly the reverse in nightime, where
the ground is colder than the atmosphere. That’s why, for example, in
nighttime you can hear the horn of an ocean-liner, which usually you can’t
hear in daytime ^_^
Question 6
• Give a few examples of animals
that use sound reflection (echoing)
to navigate or hunt for the food.
What frequencies do they use?
Whales and elephants also use
sound for communication. What
frequency do they use? Can they
use high-frequency sound wave for
communication? Please elaborate.
Q6. Echolocation
Bats and dolphins use
high-frequency sound
wave (> 20000 Hz) to
navigate and locate
for food.
They do that by
generating the sound
wave and listening
back to the reflected
sound wave from their
surrounding. As such,
they can “see” their
surrounding.
By the way, this is the
principle behind submarine’s Sound Navigation and Ranging
(SONAR) ^_^
http://animals.howstuffworks.com/mammals/bat2.htm
Infrasonic (< 20 Hz)
Communication
High-frequency sounds give lots of detail (which is important in
echolocation) but travel over a low range, while low-frequency
sounds give less details but travel over a longer range (which is
more suitable for communication).
Animals’ Hearing Frequency
Range
How ‘bout us? 
Q7. Some insects such as mosquitoes and bees produce
.
a buzzing sound.
How do they do that, and what
frequencies do they produce. Calculate the wavelengths
corresponding to those frequencies
The rapid wingbeats of the
bees
create
wind vibrations
that people hear
as buzzes.
The wing beats
at around 180500Hz, depend
on various bees
and activities .
Question 8
• The same fundamental note played
on violin sounds different from that
played on the piano or other some
other music instruments. One says
that the quality of the sound is
different. Explain in physical terms
what is happening?
Q8. Sound Timbre
(Quality/Tone)
Rather than producing only one frequency of sound wave, each music
instrument also produces other quieter but unique combination of
frequencies, called harmonics, that give rise to its characteristic sound,
i.e. its timbre
The combination of the
harmonics causing the
wave envelope to vary in
a complicated manner
(except the one produced
by the tuning fork, which
is sinusoidal).
The intensity of each
harmonics
contribution
can be analyzed using
Fourier transform (see the
next two slides for further
details).
Timbre Profile of Tuning Fork, Flute and
Clarinet
Harmonics
It is possible to superpose harmonics at different intensities
and frequencies to produce a
more complicated wave envelope (see figures beside), for
example by superposing (a)
waves of frequency f and 3f, (b)
then one more odd harmonic of
frequency 5f is added, (c) until
the synthesized curve approximates the square wave when
odd frequencies up to 9f are
added.
Here f is called the first
harmonic, 3f is called the third
harmonic, and so on. Hence is
the number 1,2,3,… in the horizontal axis of the timbre profiles
Question 9
• How can sound be used to clean an
object? Give an example.
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