Tutorial 3Tutorial 3WaveWave

Q1. In Young's double slit experiment, if Q1. In Young's double slit experiment, if we know that the distance from the we know that the distance from the center line to the first bright fringe is center line to the first bright fringe is 5cm, what is the distance from the third 5cm, what is the distance from the third to the fourth bright fringe?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 cmhttp://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).

L

x

Slit separation = d; Distance on screen = xAngle of incidence = θ

= mλ bright = (m + ½)λ dark m = 0, 1, 2, …

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 Q2. Why would it be so that our eyes did not evolve such that we can see did not evolve such that we can see

deep ultra-violet light?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 Q3) A 60 Hz vibration produces waves in air that propagate at 340 m/s. What in air that propagate at 340 m/s. What is theis theSpeed of the waveSpeed of the waveTheir frequencyTheir frequencyThe wavelengthThe wavelengthThe periodThe period

a) Speed: v = 340 m/s

b) Frequency: f = 60 Hz

c) Wavelength:

d) Period:

mf

v67.5

sf

T 0167.01

Question 4Question 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 waveSound wave

Q5Q5• Do sound waves bend towards or

away from the ground on hot day? Explain why?

Q5. Sound Speed VS Q5. Sound Speed VS TemperatureTemperature

Trvsoundinai ~

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 ^_^

Sound travel at higher temperature

)/(6.04.331)( smTv cinairsound

Question 6Question 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. EcholocationQ6. 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 sub-marine’s Sound Navi-gation and Ranging (SONAR) ^_^

http://animals.howstuffworks.com/mammals/bat2.htm

Infrasonic (< 20 Hz) Infrasonic (< 20 Hz) CommunicationCommunication

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 Animals’ Hearing Frequency RangeRange

How ‘bout us?

The rapid wing-beats of the bees create wind vibrations that people hear as buzzes.

The wing beats at around 180-500Hz, depend on various bees and activities .

.. 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

Question 8Question 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 Q8. Sound Timbre (Quality/Tone)(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 Timbre Profile of Tuning Fork, Flute and ClarinetClarinet

HarmonicsHarmonicsIt is possible to superpose har-monics at different intensities and frequencies to produce a more complicated wave en-velope (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 approxi-mates 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 hori-zontal axis of the timbre profiles

Question 9Question 9• How can sound be used to clean an

object? Give an example.

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