THE WORLD COMMUNICATES

 

WAVES:         A wave is a travelling vibration that transmits energy.

 

Most waves are mechanical. In these cases the particles oscillate about fixed points in simple harmonic motion. While doing so they transmit energy to the particles next to them so that they in turn oscillate with simple harmonic motion. In this way the energy of the wave is transmitted but the matter is not.

Electromagnetic waves consist of electric and magnetic fields oscillating at right angles to each other. Since it is not particles that are vibrating, these waves do not require a material medium in which to be transmitted and hence can travel through a vacuum.

 

The DISPLACEMENT of a particle or field in a wave refers to its distance from the mean position with its sense being stated as either positive or negative,

 

The maximum displacement of a particle from its mean position is called the AMPLITUDE, (A) of the wave.

 

The MEDIUM is the type of substance that the wave travels through.

 

A CREST of a wave is a position of maximum positive displacement of the wave particle or field while a TROUGH is a position of maximum negative displacement of the wave particle or field.

 

The WAVELENGTH, (l) of a wave is the distance between two successive crests or two successive troughs of the wave.

 

The number of complete oscillations of a particle in unit time is called the FREQUENCY, (f) of the wave. If the second is taken as the unit of time then the unit of frequency is the HERTZ, (Hz) which is one vibration per second. The frequency may also be taken as the number of complete wavelengths that pass a given point in unit time.

 

The PERIOD, (T) of a wave is the time taken for the particle or the electric and magnetic field to undergo one complete vibration. It is the time taken for one wavelength to pass a given point.

The period is the reciprocal of the frequency: T = 1/f and f = 1/T         

 

The INTENSITY, (I) of the wave refers to the amount of energy carried by the wave. It is measured at right angles to the direction of propagation (travel) of the wave and is proportional to the square of the amplitude.  I a A2 .

 

The VELOCITY, (v) of a wave refers to the displacement at which the wave is transmitted in a given time i.e. the velocity at which it travels. It is equal to the product of the length of the wave (wavelength) and the number of waves per unit time (frequency).

 

v = f l

 

Waves may be of two main types; transverse or longitudinal (compression).

 

In TRANSVERSE WAVES the particles (or electric and magnetic fields) vibrate at right angles to the direction of transmission of the wave i.e. at right angles to the direction of energy flow.

 

In LONGITUDINAL WAVES i.e. COMPRESSION WAVES the particles vibrate to and fro in the direction of transmission of the wave i.e. to and fro in the direction of energy flow. A longitudinal wave consists of a series of high pressure regions where the particles are close together (COMPRESSIONS) alternating with a series of low pressure regions where the particles are further apart (RAREFACTIONS). The wavelength of a longitudinal wave is the distance between two successive compressions or two successive rarefactions.

 

Displacement (s)                                                                       Crest   

    Trough

Sound waves are compression waves and require a medium to be transmitted. Their speed increases as the density of the medium increases. They travel fastest through solid, slower through liquids and slowest through gases. Sound will not travel through a vacuum.

 

PITCH is a subjective quality of a sound by which it is described as high or low depending on its position on a musical scale. However pitch is related to frequency and a note with a high pitch has a high frequency while a note with a low pitch has a low frequency.

 

A loud sound carries more energy than a soft sound i.e. it has a higher intensity. This means that the higher the volume of the sound the greater is the amplitude of the wave.

 

When sound hits a surface it can either be reflected or absorbed. A reflected sound is an ECHO. The distance between the reflecting surface and the person has to be at least 20 metres otherwise the time interval between the original and reflected sound is too small for the ear to distinguish them as separate. Sound tends to be reflected from hard surfaces and absorbed by soft surfaces.

 

 

 

 

THE  WORLD COMMUNICATES – REVISION QUESTIONS

 

Q.1.     A wave travels at 500 ms-1 at a frequency of 50 Hz. What is its wavelength? 

(10 m)

 

Q.2.     The wavelength of the note emitted by a 512 Hz tuning fork was found to be   64.0 cm. What was the velocity of sound under these conditions.

            (328 ms-1)

 

Q.3.     What is the velocity of the radio signal sent out by station Triple M?

            If the frequency of its signal is 104.9 MHz, what is the wavelength of its signal?

            (3 x 108 ms-1, 2.86m)

 

Q.4.     Radio station 2KA broadcasts at two different frequencies; (i) 783 kHz and (ii) 1476 kHz. What are the respective wavelengths of these signals?

            ( (i) 383m, (ii) 203m) )

 

Q.5.     What is the wavelength of light of the following colours, given their frequencies.

            (i) Blue, f = 7.0 x 1014 Hz.        (4.3 x 10-7m)

            (ii) Green, f = 5.5 x 1014 Hz      (5.5 x 10-7m)

            (iii) Yellow, f = 5.2 x 1014 Hz    (5.8 x 10-7m)

            (iv) Red, f = 4.0 x 1014 Hz.       (7.5 x 10-7m)

 

Q.6.     The wavelength of a beam of gamma rays was found to be 6.0 x 10-12 m. What was the frequency of these rays?

            (5.0 x 1019 Hz)

 

Q.7.     Two students determined the velocity of sound by the following method.

            They measured 100m from the face of a cliff and one of them stood there banging two garbage bin lids together. He gradually increased the frequency until the bangs of the lids just coincided with the echo.  The other student carefully timed 10 bangs (and 10 echoes) and obtained a result of  7.5 seconds.

            What value would they have obtained for the velocity of sound?

            (267 ms-1)

 

Q.8.     The speed of sound in air is approximately 333 1/3 ms-1. If thunder is heard 12 seconds after the flash of lightning is seen, how far away is the centre of the storm?

            (4 km)

 

Q.9.     An audio oscillator emits sound waves of frequency 510 Hz on a day when the speed of sound in air is 340 ms-1.

(i)                  What is the wavelength of the sound?

(ii)                Will the sound speed up, slow down or stay the same speed if it enters a solid wall?

( (i) 2/3 m.  (ii) speed up)

 

PROGRESSIVE  WAVES.

 

            If we have a single wave, whether it be a pulse or continuous wave, the crest or crests move in the direction of propagation of the wave. Such waves are called PROGRESSIVE WAVES because the crests progress in the direction of travel of the wave. These can be contrasted with standing waves which are formed from two identical waves travelling in opposite directions. In standing waves the crests do not move along the wave but remain in the same position.

 

            If the period of a progressive wave is T and its wavelength is l then in a time of T the crest will have moved forward a distance l.

 

                       

                        A progressive wave at time t = 0.

 

                       

`                       The same progressive wave at time t = T/4 i.e. a quarter period later.

 

EXERCISE:

 

1.                  What is the wavelength of the above wave?

 

2.                  What is the amplitude of the above wave?

 

3.                   Draw the above wave at times t = T/2, t = 3T/4, t = T and t = 5T/4.

 

4.                  If the period of the wave is 0.4 second what is the frequency?

 

5.                  What is the speed of the wave?

 

6.                  Consider a particle on the wave that has zero displacement at time t = 0.

(i)                  What is its displacement at time t = 0.1 s?

(ii)                What is its displacement at time t = 0.2s?

(iii)               What is its displacement at time t = 0.3 s?

                  t = T/2

 

                  t = 3T/4

 

                  t = T

 

                  t = 5T/4

 

ANSWERS.

 

1.                  4.0 cm.

2.                  1.0 cm

3.                 

4.                  2.5 Hz.

5.                  10 cm s-1.

6.                  (i) – 1.0 cm

(ii)zero

(iii)1.0 cm.

SUPERPOSITION:

If two or more waves reach the same point at the same time a compound wave is formed that is the sum of the individual waves.

 

If two waves travel towards each other they form a compound wave as they pass through each other and resume their original form after they have passed through.

 

Two waves approach each other from opposite directions.

 

The two crests are at the same point at the same time.                          

 

The waves have passed through each other.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Exercise:

 Each of the four diagrams below show two pulses moving towards each other at 1.0 cms-1.

Show the wave pattern formed by each pair of pulses 0.5s, 1.0s, 1.5s and 2.0s after the instant shown.

                       

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SUPERPOSITION SOLUTIONS

 

 

 

 

 

REFLECTION OF ELECTROMAGNETIC  WAVES

 

            Just as sound waves are reflected as echoes, so too do we get the reflection of electromagnetic waves. The most obvious example is the reflection of light rays by a mirror but all objects reflect light and the only reason that we can see an object is that light is reflected from it to our eyes.

 

 LAWS OF REFLECTION:

 

            The reflection of light and other electromagnetic waves can be summarised by the “Laws of reflection”.

1.                  The incident ray, the normal and the reflected ray all lie in the same plane.

2.                  The angle of incidence is equal to the angle of reflection.

 


This means that a wave will bounce off a surface at the same angle as it hit it (similar to a billiard ball hitting the side of the table and bouncing off at the same angle).

 

            Once we realise that we can only see because light is reflected off other objects we begin to appreciate the importance of the reflection of light in information transfer. Radar is a particular application of the reflection of microwaves, which is vital in communicating information about the location of aircraft or shipping when visual means are not suitable because of distance or weather conditions. Radio waves and television waves are reflected by communication satellites and enable us to receive direct broadcasts or telecasts of events on the other side of the world. Prior to the development of communication satellites radio waves were reflected off the ionosphere, an upper region of the atmosphere containing ionised air and free electrons. However, due to their higher frequency and shorter wavelength, television waves would be transmitted through the ionosphere rather than reflected off it so it was not possible to transmit television over large distances on Earth.

 

            For most purposes reflection of light from a plane mirror is most suitable. In such cases the size of the image is the same as the size of the object. However, if you want an enlarged image such as when you are applying cosmetics or shaving, then you could use a concave mirror and, provided you were inside the focal length, your face would appear bigger. A convex mirror can be used when a smaller image and consequently a greater field of vision is desired such as a car rear vision mirror or security mirrors in libraries or shops.

 

REFRACTION:

 

            Refraction of a wave refers to the bending of its path as it goes from one medium to another.  It occurs because the wave changes velocity as the medium changes.

 

LAWS OF REFRACTION:

The refraction of light and other electromagnetic waves can be summarised by the “Laws of refraction”

  1. The incident ray and the refracted ray are in the same plane as the normal and are on opposite sides of the surfsce boundary.
  2. When a wave passes from one medium to another, the sine of the angle of incidence bears a constant ratio to the sine of the angle of refraction. This ratio is known as the refractive index and is equal to the ratio of the velocity in each medium.

This law is known as Snell’s Law.

 

sin i  =  v1 = m

            sin r      v2       

                                                                                                                                                                                       

 

When a wave travels from a less dense medium to a more dense medium (e.g. from air to water) the refractive index is greater than 1.0 and the wave bends towards the normal.

 

When a wave travels from a more dense medium to a less dense medium (e.g. from water to air) the refractive index is less than 1.0 and the wave bends away from the normal.

 

When travelling from a more dense to a less dense medium a stage is reached where the angle of refraction reaches 90o i.e. the refracted wave just skims across the surface. A slight increase in the angle of incidence will see the wave refracted back into its original medium i.e. reflected. At this point the wave is reflected and the laws of reflection rather than the laws of refraction apply. Reflection of this type is known as TOTAL INTERNAL REFLECTION and the minimum angle of incidence where it occurs is known as the CRITICAL ANGLE.

REFRACTIVE INDEX QUESTIONS:

 

Q.1.     A ray of light enters a rectangular glass slab of refractive index 1.5 at an angle of incidence of 30o.  Calculate the

(i)                  angle of refraction

(ii)                angle of incidence to the opposite surface as it leaves the slab.

(iii)               angle of refraction as it leaves the slab.

(iv)              speed of light in the glass.

 

Q.2.     A ray of light enters a pool of water of refractive index 1 1/3 at an angle of 40o to the surface.  Calculate the angle of refraction and the speed of light in water.

 

Q.3.     A ray of light travels from glass (refractive index = 1.5)  to air.

 

(i)                  What is the refractive index from glass to air?

(ii)                What is the angle of refraction if the angle of incidence is 30o?

(iii)               What is the angle of refraction if the angle of incidence is 40o?

(iv)              What is the angle of refraction if the angle of incidence is 50o?

 

Q.4.     A ray of light strikes a mirror at an angle of 20o to the surface.

What is the angle of reflection?

 

Q.5.     A ray of light enters a transparent plastic rectangular prism 10 cm long and 5 cm wide at an angle of incidence of 40o.

(i) If the refractive index of the plastic is 1.40 what is the angle of refraction?

(ii) What distance is the ray displaced sideways as it leaves the prism?

 

Q.6.     A light on the bottom of a swimming pool 1.0m deep acts as a point source. The refractive index of water is 1.33. An observer watching the pool sees a circle of light at the surface.

(i)                  Explain why the observer sees a circle of light.

(ii)                What is the critical angle for a ray travelling from water to air?

(iii)               What is the radius of the circle?

 

 

 

ANSWERS:

Q.1. (i) 19o28’  (ii) 19o28’  (iii) 30o  (iv) 2 x 108 ms-1

Q.2. 28o49’  & 2.25 x 108 ms-1

Q.3. (i) 2/3  (ii) 48o35’  (iii) 74o37’  (iv) N/A (reflection) 

Q.4. 70o 

Q.5. (i) 27o20’ (ii) 1.6 cm

Q.6. (ii) 48o35’ (iii) 1.14m.

 

 

 

 

REFLECTION FROM CONCAVE AND CONVEX MIRRORS

 

Diagrams from: Physics Outlines by N. G. Warren.

 

 

THE WORLD COMMUNICATES – REVISION QUESTIONS

 

Q.7.     On the diagrams below, draw rays to show the position and nature of the image formed by a concave mirror and a convex mirror.

 

                       

Q.4.     Outline the difference between transverse and longitudinal waves.

Give an example of each.

 

Q.5.     Two types of earthquake waves are s waves, which are transverse and p waves, which are compression waves. Which of these would be detected on the opposite side of the Earth to the earthquake?  Explain your answer.

 

Q.6.     What does “laterally inverted” mean?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

IMAGES FORMED BY SPHERICAL MIRRORS

 

 

A spherical mirror as the name suggests is composed of a reflecting surface on part of a sphere.The centre of the sphere is known as the CENTRE OF CURVATURE and is represented in the following diagrams as C. If the reflecting surface faces the centre of curvature the mirror is CONCAVE (like a cave) and if the reflecting surface faces away from the centre of curvature the mirror is CONVEX.   The centre of the reflecting surface of the mirror is the POLE and a line passing through the pole and the centre of curvature is the PRINCIPAL AXIS.

For a concave mirror rays that are parallel and close to the principal axis will be reflected through one point. This point is known as the PRINCIPAL FOCUS. This is represented as F in the following diagrams and is located midway between the centre of curvature and the pole. For a convex mirror, all rays seem to come from the principal focus. The distance between the principal focus and the pole is known as the FOCAL LENGTH. 

 

            Parallel rays at different distances from the principal axis of spherical mirrors do not reflect to intersect at exactly the one point. This is known as SPHERICAL ABERRATION and can be overcome by using parabolic mirrors.

 

            Ray diagrams can be drawn to find the size and nature of the image formed by a spherical mirror. Two of the following three rays are drawn from the top of the object. The point of intersection forms the top of the image. The bottom of both the object and the image lie on the principal axis.

 

Ray 1: Drawn parallel to the principal axis then reflected through the principal focus (if concave) or produced to pass through the principal focus (if convex).

 

Ray 2:  Drawn through the principal focus then reflectedparallel to the principal axis.

 

Ray 3:  Drawn through the centre of curvature and reflecting back on itself.

 

            If the rays intersect in front of the mirror a REAL image is formed and the image can be projected onto a screen. If the rays when produced intersect behind the mirror a VIRTUAL image is formed and this cannot be projected onto a screen.

 

 

 

OBJECT BETWEEN PRINCIPAL FOCUS AND POLE.

 


 

Image: Magnified, Upright, Virtual.

 

 

OBJECT AT THE PRINCIPAL FOCUS.

 

                                    Image: Formed at infinity i.e. no image.

 

 

OBJECT BETWEEN PRINCIPAL FOCUS AND CENTRE OF CURVATURE.

 

 

Image: Magnified, Inverted, Real.

 

OBJECT AT CENTRE OF CURVATURE.

 

 

Image: Same size, Inverted, Real.

 

OBJECT OUTSIDE CENTRE OF CURVATURE.

 

 

Image: Diminished, Inverted, Real.

 

 

CONVEX MIRRORS.

 

Image: Diminished, Upright, Virtual.

 

THE WORLD COMMUNICATES – REVISION QUESTIONS

 

                  Q.1.           Name the different types of electromagnetic waves.

 

                  Q.2.           What vibrates in an electromagnetic wave?

 

                  Q.3.           What type of electromagnetic wave travels fastest in (a) vacuum?

                                                                                                             (b) water?

 

                  Q.4.           What is polarisation?

 

                  Q.5.           Briefly describe three different ways light can be polarised.

 

                  Q.6.           Can radio waves be polarised? Explain.

 

                  Q.7.           Can sound waves be polarised? Explain.

 

Q.8.     Suppose you were walking through the Rippemoff markets and you came across a stall selling “genuine polaroid sunglasses” for $1.00 a pair. Describe how you could use two pairs of sunglasses to determine if they really were polaroid.

 

Q.9.     Why is the sky blue?

 

Q.10.   What colour would you expect the sky to appear from the surface of (a) Venus?

                                                                                                                           (b) Mercury?

            Explain your answers.

 

Q.11.   Why does the Moon appear red during a total eclipse?

 

Q.12.   What do the letters C.D. and D.V.D stand for?

 

Q.13.   What is the difference between a C.D. and a D.V.D.?

 

Q.14.   What is the difference between a digital and an analogue signal?

 

Q.15.   What is “modulation” of radio signals?

 

Q.16.   What is the difference between amplitude modulation and frequency modulation of radio waves?

 

Q.17.   What does LASER stand for?

 

Q.18.   Describe three practical applications of lasers.

 

 

 

THE  LOUD-SPEAKER

 

                        The loud-speaker illustrates how a changing electric current can be converted into sound.  It consists of a powerful magnet with light cylindrical coils, known as the voice coils, mounted over the central pole piece without touching it. The output current from the radio fluctuates as it passes through the voice coil. Since the voice coil is in a magnetic field it experiences a fluctuating force that causes it to vibrate. The rigid paper cone is attached to the voice coils so the vibration is transmitted to the paper cone. This causes the air around it to vibrate and this is detected as sound.

 

                       

 

 

 

Q.19.   Outline the difference between transverse and longitudinal waves.

Give an example of each.

 

Q.20.   Two types of earthquake waves are s waves, which are transverse and p waves, which are compression waves. Which of these would be detected on the opposite side of the Earth to the earthquake?  Explain your answer.

 

Q.21.   What does “laterally inverted” mean?

 

 

 

 

 

 

 

 

 

 

TRANSFORMERS

 

Q.1.     The following diagram illustrates the general construction of a transformer.

            The number of turns in the coils is actually many hundred but for clarity only a few turns are shown here.

 

(i)                  In what way does an ideal transformer differ from a normal one?          

(ii)        Why does a transformer not work if a steady direct current is applied to the primary coil?

(iii)       Why is the core of a transformer usually made of laminated sheets of iron rather than a        square block of iron with a hole in the middle?

(iv)       Would aluminium or copper be suitable materials for the core of a transformer? Explain.

(v)        The potential difference across the primary coil is 12 volts and across the secondary coil is 240 volts. If there are 100 turns in the primary coil and 5 amps of current flows through it, how many turns are there in the secondary coil.

                        (vi)       What would be the current in the secondary coil if the transformer was ideal?

(vii)      The actual current in the secondary coil is less than the theoretical current. What happens to the lost current?

 

Q.2.     100 kW of power is to be transmitted over 100 km through cables of total resistance 10 ohms.

            (a)        Determine the power generated in the wires if it is transmitted at

(i)                  250 volts &

(ii)                 25000 volts.

(b)        Why do we refer to this power as lost power?

 

Q.3.     Smart Sally used a transformer to change 240 volts A.C. to 12 volts A.C.  Hairbrain Harry on the other hand set up the circuit below in which a resistor is used to reduce the voltage to 12 volts to operate his lamp.

 

                       

(i)                  Explain why Sally’s method of reducing the voltage is preferable to Harry’s.

(ii)                What value of resistance would Harry require?