Waves - Shawon Notes

Physics > Section 3: Waves

a) Units

3.1 use the following units: degree (°), hertz (Hz), metre (m), metre/second (m/s), second (s).

Unit of an angle: degree (o)
Unit of frequency: hertz (Hz)
Unit of distance or wavelength: metre (m)
Unit of speed/velocity: metre/second (m/s)
Unit of time-period: second (s)

b) Properties of waves

3.2 understand the difference between longitudinal and transverse waves and describe experiments to show longitudinal and transverse waves in, for example, ropes, springs and water

Waves can transfer energy and information from one place to another without transfer of matter. Waves can be divided into two types: mechanical waves and electromagnetic waves.

Mechanical waves can be of two types: transverse and longitudinal.

Transverse waves: A transverse wave is one that vibrates or oscillates, at right angles to the direction in which the energy or wave is moving. Example of transverse waves include light waves and waves travelling on the surface of water.

Longitudinal waves: A longitudinal wave is one in which the vibrations or oscillations are along the direction in which the energy or wave is moving. Examples of longitudinal waves include sound waves.

Transverse wave don’t need medium to move. Longitudinal wave needs medium to move.

Experiment: To show different types of waves in spring.

Transverse:

If you waggle on end of a slinky spring from side to side you will see waves travelling through it. The energy carried by these waves moves along the slinky from one end to the other, but if you look closely you can see that the coils of the slinky are vibrating across the direction in which the energy is moving. This is an example of transverse wave.

Longitudinal:

If you push and pull the end of a slinky in a direction parallel to its axis, you can see energy travelling along it. This time however the coil of the slinky are vibrating in direction that are along its length. This is an example of longitudinal wave.

3.3 define amplitude, frequency, wavelength and period of a wave

Amplitude: The maximum movement of particles from their resting position by a wave is calleds its amplitude (A).

Wavelength: The distance between a particular point on a wave and the same point on the next wave (for example, from crest to crest) is called the wavelength (λ).

Frequency: The number of waves produced each second by a source, or the number passing a particular point each second is called frequency ( f).

Period: The period of a wave is the time for one complete cycle of the waveform.

3.4 understand that waves transfer energy and information without transferring matter

Waves are means of transferring energy and information from place to place. These transfers take place with no matter being transferred. Mobile phones, satellites etc. rely on waves.

Example: If you drop a large stone into a pond, waves will be produced. The waves spread out from the point of impact, carrying to all parts of the pond. But the water in the pond does not move from the centre to the edges.

3.5 know and use the relationship between the speed, frequency and wavelength of a wave:

wave speed = frequency × wavelength
v = f× λ

3.6 use the relationship between frequency and time period

frequency = 1 / time-period
f = 1/T

3.7 use the above relationships in different contexts including sound waves and electromagnetic waves

As all wave share properties the above relations can be used for any type of wave.

3.8 understand that waves can be diffracted when they pass an edge

Diffraction is the slight bending of waves as it passes around the edge of an object.

3.9 understand that waves can be diffracted through gaps, and that the extent of diffraction depends on the wavelength and the physical dimension of the gap.

The amount of diffraction depends on the relative size of the wavelength of light to the width of the gap. If the gap is much larger than the wave's wavelength, the bending will be almost unnoticeable. However, if the two are closer in size or equal, the amount of diffraction is at its highest.

c) The electromagnetic spectrum

3.10 understand that light is part of a continuous electromagnetic spectrum which includes radio, microwave, infrared, visible, ultraviolet, x-ray and gamma ray radiations and that all these waves travel at the same speed in free space

The electromagnetic spectrum is a continuous spectrum of waves which includes the visible spectrum.

  1. they all transfer energy
  2. they are all transverse waves
  3. they all travel at speed of light in vacuum (3x108 m/s)
  4. they can all be reflected, refracted and diffracted

3.11 identify the order of the electromagnetic spectrum in terms of decreasing wavelength and increasing frequency, including the colours of the visible spectrum

The list follows with increasing frequency and decreasing wavelength.
Radio Waves > Microwaves > Infra-red > Visible light > Ultraviolet > X-rays > Gamma rays
A mnemonic can help: Run Miles In Very Unpleasant eXtreme Games.

Colours of the visible spectrum

There are seven colours in the visible spectrum: red, orange, yellow, green, blue, indigo and violet. Red has the longest wavelength and lowest frequency.

A mnemonic can help: Richard Of York Gave Battle In Vain

3.12 explain some of the uses of electromagnetic radiations, including:

Radio waves: It is used in communicating information. This can be speech, radio and television, music and encoded messages like computer data, navigation signals and telephone conversations. The properties that make radio waves suitable for communicating are:

  • Radio waves can travel quickly.
  • Can code information.
  • Can travel long distance through buildings and walls.
  • It is not harmful.

Microwaves: Microwaves are used in microwave oven which cooks food more quickly than in normal oven. Microwaves are also used in communications. The waves pass easily through the Earth’s atmosphere and so are used to carry signals to orbiting satellites. From here, the signals are passed on to their destination. Messages sent to and from mobile phones are also carried by microwaves.

Infrared: Special cameras designed to detect infra-red waves can be used to create image even in the absence of visible light. Infra-red radiation is also used in remote controls for televisions, videos and stereo systems. Moreover it is used in heating materials like heater.

Visible light: The main use of visible light is to see. Visible light from lasers is used to read compact discs and barcodes. It can also be sent along optical fibres, so it can be used for communication or for looking into inaccessible places such as inside of the human body. Furthermore, it has uses in photography too.

Ultraviolet: Some chemicals glow when exposed to UV light. This property of UV light is used in security markers. The special ink is invisible in normal lights but becomes visible in UV light. UV light is also used in fluorescent lamps, to kill bacteria, to harden fillings and disco ‘black’ lights. Some insects can see into the ultraviolet part of spectrum and use this to navigate and to identify food sources.

X-rays: X-ray is used to take pictures of patient’s bone to determine any fracture. X-rays are also used in industry to check the internal structures of objects-for example: to look for cracks and faults in buildings or machinery- and at airport as part of the security checking procedure.

Gamma rays: They are used to sterillise medical instruments, to kill micro-organisms so that food will keep for longer and to treat cancer using radiotherapy.

3.13 understand the detrimental effects of excessive exposure of the human body to electromagnetic waves, and describe simple protective measures against the risks.

Microwaves: Micro waves might cause internal heating of body tissue. For this microwave ovens have metal screens that reflect microwaves and keep them inside the oven. It also has perceived risk of cancer.
It can be prevented by closing oven doors and using hands-free cell phones.

Infrared: The human body can be harmed by too much exposure to infra-red radiation, which can cause skin burning and cell damage.
It can be prevented by avoiding hot places, using reflective clothing and avoiding exposure to sun.

Visible light: Visible light can cause eye damage.
It can be prevented by sun glasses and avoiding exposure to the sun.

Ultraviolet: Overexposure of ultraviolet light will lead to sunburn and blistering. This can also cause skin cancer and blindness.
Protective goggles or glasses and skin creams can block the UV rays and will reduce the harmful effects of this radiation.

X-rays: X-ray has risk of cancer and cell damage.
Lead shielding, Monitor exposure (film badge), protective clothing can be used to prevent the risk.

Gamma rays: Gamma rays can damage to living cells. The damage can cause mutations in genes and can lead to cancer.
Lead shielding, Monitor exposure (film badge) can be used to prevent the risk.

d) Light and Sound

3.14 understand that light waves are transverse waves which can be reflected, refracted and diffracted

Light waves are transverse wave that is emitted from luminous or non-luminous objects. Light waves are transverse wave and like all waves, they can be reflected, refracted and diffracted.

3.15 use the law of reflection (the angle of incidence equals the angle of reflection)

The law of reflection states that:

  1. The incident ray, reflected ray and normal all lie in the same plane.
  2. The angle of incidence is equal to the angle of reflection.

3.16 construct ray diagrams to illustrate the formation of a virtual image in a plane mirror

Types of images:

Virtual images: Image through which the rays of light don’t not actually pass is called virtual image. Example: Image formed in the mirror. Virtual images cannot be produced on a screen.

Real images: Images created with rays of light actually passing through them are called real images. Example: cinema screen.

Properties of an image in a plane mirror

  • The image is as far behind the mirror as the object is in front
  • The is the same size as the object
  • The image is virtual – that is, it cannot be produced on a screen
  • The image is laterally inverted – that is, the left side and right side of the image appear to be interchanged.

Constructing ray diagrams

Things we include in ray diagrams of a plain mirror: object, observer's eye or some indication, plane mirror, image and rays passing object and image.

3.17 describe experiments to investigate the refraction of light, using rectangular blocks, semicircular blocks and triangular prisms

As a light ray passes from one transparent medium to another, it bends. This bending of light is called refraction. Refraction occurs due to having different speed of light in different medium. For example, light travels slower in glass than in air. When ray of light travels from air to glass, it slows down as it crosses the boundary between two media. The change in speed causes the ray to change direction and therefore refraction occurs. Example:

The light bends towards the normal as it passes from low-density to high-density(air to glass). The light is refracted and upon emerging from the glass the light bends away from the normal as it passes high density to low-density (glass to air).

Experiment: To demonstrate the refraction of light through a piece of glass block.

Apparatus: Rectangular glass block with one face frosted, two rays boxes, piece of paper, protractor.

Procedure:

  1. Place the glass block on a piece of paper with the frosted side down.
  2. Send two narrow rays of light through the glass block as shown in Figure.
  3. Observe the paths of the two rays of light.
  4. Vary the angle of incidence i and measure the angle of refraction r using protractor.

3.18 know and use the relationship between refractive index, angle of incidence and angle of refraction:

The ratio between sine of the angle of incidence and the sine of the angle of refraction is called refractive index. In a material, the refractive index is constant throughout the circuit.

n = sin i / sin r
refracive index = sin(incident angle) / sin(refracted angle)

  • Lighter mediums means that light can pass easily/ speed of light is more.
  • Dense/light doesn’t mean physical density rather than optical condition.
  • Refraction takes place in second medium.
  • The ratio from a vacuum to a denser medium is called absolute refractive index.
  • The ratio from a medium to another medium is called relative refractive index.
  • It doesn’t have a unit because it is the ratio of same curve.
  • Wavelength decreases in a denser medium, thus decreasing speed.
  • The higher the wavelength, the more the light will bend.
  • The higher the wavelength, the less the angle of refraction.

3.19 describe an experiment to determine the refractive index of glass, using a glass block

Experiment: To determine the refractive index of glass, using a glass block.

  1. Put the glass block on an wooden table which is passed by a white sheet.
  2. The border of the block is marked by a pencil.
  3. At one border draw a normal and draw three lines to use as incident ray.
  4. Set a ray box through anyone of the lines.
  5. The ray travels and passes through the glass block and finally emerges from the glass block.
  6. The passage of the ray is marked by putting some pins.
  7. Now move the glass block and gain the footprints of the pins to show the passage of the ray.
  8. Now using a protractor measure the ∠i and ∠r.
  9. Now using, = sin i/sin r ; calculate refractive index.

Ways to improve result:

  1. Repeat the experiment, and find the average reading.
  2. Plot a graph of sin I against sin r and find the gradient.
  3. Vary the value of i and repeat.

3.20 describe the role of total internal reflection in transmitting information along optical fibres and in prisms

Total internal reflection: When light falls on the surface of a lighter medium from denser medium at an angle of incidence greater than critical angle, then the light does not refracts. It rather reflects in the self-medium. This type of reflection is called total internal reflection.

Condition of total internal reflection:

  1. Light should fall in the surface of lighter medium from denser medium.
  2. Angle of incidence must be greater than the critical angle.

Uses of total internal reflection:

The prismatic periscope

Light passes normally through the surface AB of the first prism (that is, it enters the prism at 90oo. The critical angle for glass is 42o so the ray is totally internally reflected and is turned through 90o. On emerging from the first prism the light travels to a second prism which is positioned such that the ray is again totally internally reflected. The ray emerges parallel to the direction in which it was originally travelling.

The final image created by this type of periscope is likely to be sharper and brighter than that produced by a periscope that uses two mirrors. Because in mirrors, multiple images are formed due to several partial internal reflections at the non-silvered glass surface of the mirror.

Optical fibres

Optical fibre uses the property of total internal reflection. This is very thin strand composed of two different types of glass. The inner core is more optically dense than the outer one. As the fibres are narrow, light entering inner core always strike the boundary of the two glasses at an angle greater than critical angle. This technique is used to send information very fast at the speed of light.

Optical fibres are used in endoscopes and telecommunications.

3.21 explain the meaning of critical angle c

Critical angle is an incident angle at which the incident ray is refracted and the refracted angle is equal to 90 degree in condition that the light falls on the surface of a lighter medium from denser medium.

3.22 know and use the relationship between critical angle and refractive index:

sin c = 1/n
sin (critical angle) = 1/ refractive index

3.23 understand the difference between analogue and digital signals

To send a message using a digital signal, the information is converted into a sequence of numbers called a binary code. Digital electrical signals can either have of only two possible values (typically 0v and 5v). These represent the digits 0 and 1 used in the binary number system.

In the analogue method, the information is converted into electrical voltages and current that vary continuously.

3.24 describe the advantages of using digital signals rather than analogue signals

  • Regenerating digital signal creates a clean accurate copy of the orginal signal but analogue signal are corrupted by other signals.
  • With digital signal, you can broadcast programs over the same frequency. In analogue signal you need wider range of frequency to broadcast.
  • Digital systems are generally easier to design and build than analogue systems.

3.25 describe how digital signals can carry more information

Digital signals are capable of carrying more information than analogue signals because digital signals make use of the bandwidth more efficiently by closely approximating the original analogue signal. The parts of the signal that do not carry any information are thrown out thus saving the bandwidth from being used needlessly. Also, depending on the coding process, digital signals are much more efficient at filtering out noise than are analogue signals, which do not filter out noise at all thus saving even more bandwidth.

3.26 understand that sound waves are longitudinal waves and how they can be reflected, refracted and diffracted

Sound waves are longitudinal waves. Like other waves they can also be reflected refracted and diffracted. Sound waves reflect when they bounce back from a surface so that the angle of incident is equal to the angle of reflection. A reflected sound wave is called an echo. Sound waves refract when it changes direction while travelling across a high dense medium. Sound waves are diffracted when they spread while travelling through a narrow space such as doorway.

3.27 understand that the frequency range for human hearing is 20 Hz – 20,000 Hz

An average person can only hear sound that have a frequency higher than 20Hz but lower than 20000 Hz. This spread of frequency is called audible range. Frequency higher than 20000 Hz which cannot be heard by humans are called ultrasounds. Frequency lower than 20 Hz that cannot be heard by humans are called infrasound.

3.28 describe an experiment to measure the speed of sound in air

Experiment: To measure the speed of sound by direct method

Apparatus: Starting pistol, stopwatch, measuring tape.

Procedure:

  1. By means of measuring tape, observers are positioned at known distance apart in an open field.
  2. First observer fires a starting pistol.
  3. Second observer seeing the flash of the starting pistol, starts the stopwatch and then stops it when he hears the sound. The time interval is then recorded.

Ways to improve:

  1. Repeat the experiment a few times and compute the values of the speed of sound for each experiment. Find the average value. This procedure minimizes random errors in finding the time interval between seeing the flash and hearing the sound.
  2. Observers exchange positions and repeat experiment. This procedure will cancel the effect of wind on the speed of sound in air.

3.29 understand how an oscilloscope and microphone can be used to display a sound wave

When sound waves enter the mircrophone, they make a crystal or a metal plate inside it vibrate. The vibrations are changed into electrical signals, and the oscilloscope uses these to make a spot which moves up and down on the screen. It moves the spot steadily sideways at the same time, producing a wave shape called waveform.

The waveform is really a graph showing how the air pressure at the microphone varies with time. It is not a picture of the sound waves themselves: Sound waves are not transverse (up and down).

Oscilloscopes are instruments used to show waveforms of electrical signals.

When we speak in microphone, sound waves are converted into electrical signals. When we connect the microphone to the oscilloscope then the oscilloscope would display waveforms onto the screen. The waveforms are a representation of sound waves.

3.30 describe an experiment using an oscilloscope to determine the frequency of a sound wave

Experiment: To determine the frequency of a sound wave

  1. Sound is produced by a loudspeaker.
  2. The microphone catches the sound and transmits it into electrical signal.
  3. The electrical signal is feed to the oscilloscope.
  4. The oscilloscope displays the electrical signal as wave pattern.
  5. The time base knob is adjusted for value 5 ms per division.
  6. Now count the number of division occupied by one cycle of the wave.
  7. Calculate the time for one cycle (T).
  8. Now, frequency, f=1/T

3.31 relate the pitch of a sound to the frequency of vibration of the source

The more something vibrates the higher frequency.
The higher frequency, the higher pitch.
So the more vibrations the higher pitch.

3.32 relate the loudness of a sound to the amplitude of vibration.

The bigger the vibration the higher the amplitude.
The higher the amplitude the louder the sound.

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