Unit 1 Worksheet
Unit 1 Worksheet Answers
Unit 1.3.5 Doppler Effect Worksheet
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Unit 2 Worksheet
Unit 2 Worksheet Answers
Final Worksheet
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Final Worksheet

1. (a) Discuss the relationship between intensity and loudness of sound and how loudness is measured.
(b) When I play my stereo, I try to ensure that the intensity does not exceed 20 dB in the road. My neighbour's stereo is measured at 50dB in the same road area. How many more times is the intensity of the sound from the neighbour compared to my stereo ?

Answer:
(a) Loudness is the psychological reaction to (or perception) of a sound, whereas intensity refers to the transfer of energy by the wave. Intensity of sound waves is defined as the average energy transported per second per unit area perpendicular to the direction of propagation and is measured in Wm-2. Loudness of a tone depends on frequency as well as intensity as all ears are not equally sensitive to sounds of all frequencies. Sounds of the same intensity but different frequencies are often perceived as having different loudness.
To measure loudness, we have to relate a subjective quality such as loudness to a physical quantity such as intensity . Consider a point source emitting sound waves of power W, equally in all directions. Assuming that the wave spreads out so that the energy follows the inverse square law so that 
r ∝ 1/A2.
By definition, the intensity I of a wave, or the power per unit area is the rate at which the energy transported by the wave transfers through a unit area A perpendicular to the direction of travel of the wave.
I = (Poweravg)/A.
The energy emitted by the source passes through a sphere of radius r, so the average power emitted by the source must be distributed uniformly over each spherical wave front of area 4πr2.

Then Intensity becomes I = [Poweravg] /[4πr2]

The Intensity I follows the inverse square law, so that I ∝ 1/A2

The symbol β is used for sound intensity and Io is the reference intensity. Io is defined as the threshold of hearing and has the intensity 1.00 X 10-12 Wm-2.

β = 10 log [I/Io]

The intensity of sound β is measured in units called decibels (dB). Loudness is the brain's interpretation response to both the intensity and frequency of the sound. As a general rule an increase in sound level of 10 dB is interpreted as doubling of the loudness but is relatively inaccurate at very low or very high frequencies.

(b)
ans

2. (a) Discuss how are tension and length related to the fundamental frequency of the vibration produced by a stretched string? A guitar string 1.00 m long has mass 10.00 g.
(b) How much tension must the string be under if it is to vibrate at a fundamental frequency of 131 Hz?
(b) What is the frequency of the first harmonics? You may use the equation that μv2 = FT.

(a) If the ends of the string are fixed, they will be nodes at both ends. The fundamental frequency of a stretched string is such that the wavelength is twice the length of the string. This gives f = V/2L where V is the velocity of the wave on the string and L is the length of the string. Increasing the tension increases the fundamental frequency and increasing the length decreases the frequency by the square of L as fo = [(FT)/(4μL2)].

ans ans
wavelength of fundamental frequency of a stretched string
wavelength of the first harmonics


The Velocity formulawhere FT is the tension of the string and μ is the mass per unit length.

The tension on the string FT = μv2.

(b) FT = μ(2fL)2.

FT = {[(1X10-2kg)/1.00m] [(2X131HzX1.00m)2]}.

FT = 686N.

(b) Thus the fundamental frequency fo = V/2L

The first harmonic f1 = V/L

f1 = 2fo

f1 = 262 Hz.

 

3. (a) Discuss the evidence that EMR have both a wave and particle nature.
(b) Discuss the properties of the electromagnetic spectrum with emphasis on wavelength and frequency.
(c) Calculate the wavelength of a beam of visible red light from a laser with a frequency 5 X 1014 Hz. Use the speed of light as 3 X 108 ms-1.          

(a) EMR as a Particle can have particle-like interactions (i.e. collisions) with electrons and other particles.
1. The photoelectric effect: A photon may knock an electron out of an atom and in the process the photon disappears. EMR can have momentum, which is related to the frequency f and wavelength λ of the electromagnetic wave by P = hf/c or P = h/λ where P = momentum, h = Planck's constant, f = frequency of the EMR, c = sped of EMR, and λ = wavelength of EMR. The photon may knock an atomic electron to a higher energy state in the atom if its energy is not sufficient to knock the electron out altogether. In this process the photon also disappears, and all its energy is given to the atom. Such an atom is then said to be in an excited state.
2. The photon can be scattered from an electron (or a nucleus) and in the process lose some energy; this is the Compton effect. But notice that the photon is not slowed down. It still travels with speed c, but its frequency will be lower because it has lost some energy.
3. If a detector is place to check which slit the photon passes through in the interfere experiment the bands disappear. Particles behave this way according to Heisenberg's Uncertainty principle.
4. Pair production: A photon can actually create matter, such as the production of an electron and a positron (positron has the same mass as an electron, but the opposite charge),

EMR as a Wave has frequency, wavelength, amplitude, and other properties inherent in wave mechanics.
1. Thomas Young showed that EMR from a narrow single slit when passed through a pair of narrow slits is diffracted as if the the EMR were individual sources of EMR. When a single slit was opened, it merely impacted the observation screen with greater intensity at the center and then faded as you moved away from the center. It was observed that the EMR waves show interference under the principle of superposition, creating constructive interference (light bands) and destructive interference (dark bands). As particles, the intensity of both slits should be the sum of the intensity from the individual slits.
Interference - When it encounters the slits, it passes through and divides into two wave fronts. These wave fronts overlap and approach the screen to produce interference patterns.
2. An EMR source can be set up to emit one photon at a time. When such a source is used in Young's double slit experiment, an interference pattern is still observed, and cannot be explained by the particle theory.
3. Diffraction - EMR shows diffraction patterns one would expect from waves.

(b) The electromagnetic spectrum is a wide range of different electromagnetic (EM) waves. EM waves don't need a a material for them traveland so can travel across the great vacuum of space from distant stars and planets. Electromagnetic waves are named for the fact that they have both an electric and a magnetic component. Wm waves consist of electric and magnetic fields are perpendicular to each other and to the direction of travel. The electric and magnetic fields are in phase. They are transverse waves. They are field waves NOT matter waves and so can propagate in empty space.

The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation.


Increasing frequency

Increasing wavelength
Gamma-Rays
Have the highest frequencies and shortest wavelengths may in fact be identical to an x-ray but the terms x-ray and gamma rays are statements about origin rather than implying different kinds of radiation.
X-ray
Highly penetrating rays which emanated when high energy electrons struck a metal target
Ultraviolet

Tissue effects of ultraviolet include sunburn, but can have some therapeutic effects as well. The eyes are quite susceptible to damage from ultraviolet radiation. Tthe sun is a strong source of ultraviolet radiation, but atmospheric absorption eliminates most of the shorter wavelengths.

Visible Light

The narrow visible part of the electromagnetic spectrum corresponds to the wavelengths near the maximum of the Sun's radiation curve. In interactions with matter, visible light primarily acts to elevate electrons to higher energy levels. White light may be separated into its spectral colors by dispersion due to refraction

Infrared

A broad range of frequencies, beginning at the top end of those frequencies used for communication and extending up the the low frequency (red) end of the visible spectrum. The wavelength range is from about 1 millimeter down to 750 nm. Adjacent to the visible spectrum is called the "near infrared" and the longer wavelength part is called "far infrared". In interactions with matter, infrared primarily acts to set molecules into vibration. Does not penetrate the atmosphere well.

Microwaves

Are good for transmitting information from one place to another because microwave energy can penetrate haze, light rain and snow, clouds, and smoke. Shorter microwaves are used in remote sensing. These microwaves are used for radar like the doppler radar used in weather forecasts. Cause water and fat molecules to vibrate, which makes the substances hot.

Radio waves

Are also given off by stars, sparks and lightning, which is why you hear interference on your radio in a thunderstorm. Radio waves are the lowest frequencies in the electromagnetic spectrum, and are used mainly for communications.

Long waves
Long Wave - around 1~2 km in wavelength.

 

(c) λ = v/f
λ = (3 X 108 ms-1)/ (5 X 1014 Hz)

λ = 6 X 107 m.

λ = 600 nm.

4. (a)Discuss the formation of images by plane and spherical mirrors.
(b)Two flat mirrors are perpendicular to each other. An incoming beam of light makes an angle of 30° with the first mirror as shown the diagram.  What angle will the outgoing beam make with the second mirror? 
ans

(a)

/ Inverted
ansImage in Plane Mirrors.
Object distance Image distance Type of image SizeInverted
All
= Object distance
Virtual
Same
Lateral
/ Inverted
ansImage in Concave Mirrors.
Object distance Image distance Type of image SizeInverted
Object distance > c
f > Image distance < c
Real
Diminished
Yes
Object distance = c
Image distance = c
Real
Same
Yes
f > Object distance <c
c > Image distance
Real
Magnified
Yes
Object distance = f
Real
Magnified
Yes
Object distance < f
Behind the mirror
Virtual
Magnified
No
/ Inverted
ansImage in Convex Mirrors.
Object distance Image distance Type of image SizeInverted
All
> f behind the mirror
Real
Diminished
No

(b)ans
60°.

5. Discuss the four major kinds of interactions when photons pass through matter and their applications in development of technology.

1. The photoelectric effect: This happens when a photon knocks an electron out of an atom resulting in the disappearance of the photon. Directing a beam of light of certain short wavelength onto a clean metal surface causes electrons to be ejected from the surface. 
— The energy of the photons is given by the equation E = hf, where h = Planck's constant and f the frequency of the radiation.
— The maximum kinetic energy (of the most energetic ejected electrons) does not depend on the intensity of the light source. In classical physics the energy of the ejected electron should vary with the energy of the light wave (amplitude of the wave). The energy of the photons is given by the equation E = hf (quantum mechanics), so the maximum energy given to an electron depends on the frequency and not the intensity (in classical physics) 
—There is a cut-off frequency under which electrons are not ejected no matter how intense the radiation. In classical physics electrons should be ejected for all frequencies if the intensity is great enough. The energy of the photons is given by the equation E = hf (quantum mechanics), so the maximum energy given to an electron depends on the frequency and not the intensity (in classical physics). To escape from the atom the electron must acquire a certain minimum energy called the work function (Φ). Electrons can only escape if hf > Φ.

2. Excitation: The photon may knock an atomic electron to a higher energy state in the atom if its energy is not sufficient to knock the electron out altogether. In this process the photon also disappears, and all its energy is given to the atom. Such an atom is then said to be in an excited state.
— Heated solids, liquids and dense gases emit light with a continuous spectrum of wavelengths. This radiation is assumed to be due to oscillations of atoms and molecules, which are largely governed by the interaction of each atom or molecule with its neighbors. Rarified gases on the other hand when excited to emit light do so at only certain wavelengths giving rise to line spectra rather than continuous spectra which are specific top the material. the opposite or absorption spectra are observed when continuous spectra are passed through the same materials.
— In rarified gases (low density) the light emitted or absorbed are by individual atoms rather than interacting atoms.
— The Balmer series of spectral lines for hydrogen is shown on the left.
The Lyman series (in the UV region) and Pashen series (in the IR region) show the same patterns.
— These can only be explained with quantum physics as the classical physics of the Rutherford model cannot explain them, quite apart from the obvious difficulties of a charged particle (electron) rotating in an electric field without emitting light and spiraling into the nucleus.

3. Compton Effect: Sometimes the photon is scattered from an electron or nucleus lose some energy in the process. However, the photon is not slowed down as its speed is still c. As it has lost some energy its frequency must be lowered (recall E = hf).
— Compton directed a beam of X-rays of a particular wavelength to a carbon target. The scattered X-rays contained a range of wavelengths with two prominent peaks for every angles observed.
— However, classical physics could not explain the scattering of x-rays as the scattered rays should have the same wavelength and frequency as the incident rays.
— This has extended the concept of photons to also possess linear momentum. When a photon interacts with matter, it behaves as a collision in the classical sense with the conservation of Energy and Momentum.

4. Pair production: A photon can actually create matter, such as the production of an electron and a positron. (Recall: A positron has the same mass as an electron, but the opposite charge,)
— In pair production, the photon disappears in the process of creating the electron–positron pair. This is an example of 
— Mass is being created from pure energy in accord with Einstein’s equation E = mc2 (the photon cannot create an electron only as electric charge would not then be conserved.)
— If a positron comes close to an electron, the two quickly annihilate each other and their energy, including their mass, appears as electromagnetic energy of photons (the inverse of pair production)
— Positrons are rarer than electrons nature so they do not last long. 
— since the electron and positron move in the same direction along one of the axes, pair production must have a massive object (compared to the photon) like a nucleus to carry momentum in the opposite direction (Law of conservation of Momentum) 

Some applications of the above effects are:
— Electron–positron annihilation is the basis for the type of medical imaging known as PET.
— Nuclear medicine
— Burglar alarms and automatic doors often make use of the photocell circuit
— Photocells are used in many devices, such as absorption spectrophotometers, to measure light intensity.
— Semiconductors

     
Concept by Kishore Lal. Programmed by Kishore Lal... Copyright © 2015 Kishore Lal. All rights reserved.