WAVES, SOUND AND LIGHT – GRADE 11 –

Geometrical optics - Lenses - Two general types of lenses

1) Converging (convex) lenses 2) Diverging (concave) lenses

- Converging lenses bring light rays - Diverging lenses spread light rays out together (parallel beams will (cause parallel beams to diverge converge TO a point) FROM a point) - Are always thicker in the middle - Are always thicker at the edges

- A lens can be considered to consist of a large number of prisms- Refraction occurs as the light rays move through a medium of different optical density- There is zero refraction at the middle of the lens as light passes straight through (on the normal)- As the light is incident on the first side of the lens, refraction towards the normal occurs.- As light moves out of the prism, refraction away from the normal occurs.- The rays either meet at a point (convex lens) or they appear to emanate from a point (concave)

Definitions:- Optical centre (O): The centre of the lens- Principal / optical axis (AB): The lines joining the centers of

curvature

- Focal point (F): The point at which the rays converge (convex lens) or

the point from which the rays diverge (concave lens)- Focal length (f): The distance between the optical centre and the focal

point

Note: The same definitions and terminology hold for a concave lens

Types of images

http://dev.physicslab.org/asp/applets/opticsbench/default.asp

- There are two types of images that can form (REAL or VIRTUAL)- a REAL image - formed when light rays pass through (actually go to) and diverge from

the image - can be displayed on a screen

- a VIRTUAL image - formed when light rays DO NOT pass through the image point but only appear to diverge from the image point

- cannot be displayed on a screen

* See note on drawing ray diagrams *

- The following factors need to be stated when describing an image…1) Image REAL or VIRTUAL?2) Image UPRIGHT or INVERTED with regards to the object?3) Image LARGER (magnified) or SMALLER (diminished) compared to object?

- The human EYE

- The eye uses a 2 lens system - The cornea and aqueous humour form a fixed lens- While the other lens is able to be manipulated by the attached ciliary muscles- The light rays are focused onto the retina, forming an image (what type?)- The iris is a ring of muscles that controls the size of the pupil- The size of the pupil in turn, controls the amount of light entering the eye- The eye needs to be able to see both distant, as well as close objects- Thus the focal length of the lens needs to be altered- This is done by the ciliary muscles that make the lens more or less convex

http://www.google.co.za/search?hl=en&source=hp&q=how+the+human+eye+works&meta=&aq=f&oq=

- Eye Defects 1) Astigmatism - Either the cornea or the lens is NOT exactly spherical (not uniform) - One part of an object will be clearly focused, while another is blurred

2) Loss of accommodation (presbyropia) - Can’t see distant or close objects - Need bifocals to correct - One lens for distant objects and the other for close objects

3) Myopia (short sightedness)- Can see nearby objects clearly- Distant objects blurred- Lens refracts the image of a far object too much, thus the image doesn’t fall sharply on the retina- A concave lens is needed to correct vision

4) Hyperopia (far sightedness)

- Can see distant objects clearly- Nearby objects blurred- Lens refracts the image of a nearby object too little, thus the image is focused behind the retina- A convex lens is required to correct for this defect

Difference between a microscope and telescope?

- A compound microscope consists of a 2 lens system (both convex)- Both lenses have very short focal lengths and are aligned along the same principle axis- The lens closest to the actual object is called the OBJECTIVE- While, the lens closest to the eye is called the OCULAR or EYEPIECE- The object is placed between F and 2F of the Objective- This causes the formation of a real, inverted and enlarged image

- The real image formed by the objective (lens) acts as an object for the eyepiece (lens)- The eyepiece is positioned in such a way that the real image (the new object) is placed between the lens and principal focal length of the eyepiece- This causes the formation of a virtual, ENLARGED image

- Compound microscope

The combined ray diagram would look as follows…

Describe the image… 1) Virtual 2) Inverted 3) Enlarged

- Telescope - There are many types of telescopes - The two most common are the Astronomical telescopes (refracting) and the mirror telescopes (reflective) - A telescope also uses a 2 lens system (also both convex) - Parallel rays (because the object is far away) come from a far away object - These rays pass through the objective (lens) and form a real, inverted and diminished image at the focal point (FObjective) of the objective

- Thus real image acts as an object for the second lens (ocular)- The eyepiece is placed so that the new object is positioned on the focal length of the eyepiece (Feyepiece) - This results in the formation of a virtual, ENLARGED image

Magnifying power =Long focal length

Short focal length

The combined diagram would look as follows (note the position of the focal lengths)…

Note: Find some information on SALT (South African Large Telescope)

Longitudinal waves - A longitudinal wave is a wave where the displacement of the medium is PARALLEL to the direction of propagation of the wave

- Terminology - Wavelength The distance between any two points that are in phase

Note: A longitudinal wave is made up of a succession of compressions (the particles of the medium are close together) and rarefaction (particles of the medium are furthest apart)

- Amplitude (A): Maximum displacement of the medium from rest position

fT 1Tf 1

fvTv

- Period (T): The time taken for a complete wave to pass a point in the medium (unit: s)- Frequency (f): The number of complete waves passing a point in the medium (unit: Hz)- Relationship between the frequency and the period of a wave…

or

- The speed of a longitudinal wave (v) is given by the wave equation…

or

- Particle position, displacement, velocity and acceleration - When a longitudinal wave moves through a medium, each particle in the medium moves backwards and forwards and returns to its rest position - Consider the diagram below that represents the coils of a spring in their rest position compared to when a longitudinal wave is moving through the spring…

- How sound is created - All sound is produced as a result of a vibration - Energy is needed to produce the vibration - Sound cannot travel through a vacuum, it needs a medium - It moves best through solids, then liquids and worst through gasses - Sound waves exist as longitudinal waves - It is transmitted along the particles of the air as a series of compressions and rarefactions

Sound and sound waves

- Pitch, loudness and quality (tone) - A useful piece of equipment to use when investigating sound waves is an OSCILLOSCOPE (Graphical representation of a sound wave)

- The AMPLITUDE of a sound wave gives an indication of the loudness

- The FREQUENCY of a particular note indicates the pitch of the note- A higher frequency (shorter wavelength) has a higher pitch- Consider in the diagram below that both the notes have the same loudness, but they have different pitches

- The NUMBER of OVERTONES (or harmonic tones) that is heard with the fundamental frequency determines the quality of the note

- Noise and music

- A musical note is caused by REGULAR vibrations - The sound wave for a noise has no particular repetitive form - The unit for sound intensity is called the Decibel (dB) - Sound becomes painful for the human ear when it exceeds 120dB (pain threshold)

The Human ear and hearing - The ear is made up of 3 regions – outer, middle and inner ear

- Sound waves move through the particles in the air, causing a succession of compressions and rarefaction- These are directed into the ear and down the ear canal, where the variations cause the ear drum to vibrate

- These vibrations are intensified as they move along tiny bones in the middle ear and onto the oval window - The vibrations are converted into an electrical impulse in the cochlea and sent to the brain along the auditory nerve

Properties of sound and their application

- Like other waves, sound waves can undergo reflection, refraction and resonance

Reflection- Reflections of sounds are often called “ECHOES”- The law of reflection still applies- Uses: - ultra sound

- Bats navigate- Sonar

- Ultrasound - Ultrasound ranges from approximately 20kHz to 100kHz - Waves in this particular frequency range are used in medical diagnosis - Different types of human tissues (eg. Bone, fat, muscle) have different reflective properties for high frequency waves - When a particular region of the body is scanned, part of the wave will be reflected (echoes) and the rebounding waves are recorded and used to form a picture on a screen (other part is transmitted)

NOTE: Investigate the mechanism, application and functioning of SONAR

http://www.youtube.com/watch?v=3G219nsWz0o

Refraction- The temperature of air influences the speed of sound- Sound moves faster through warm air than cold air- Sound waves bend (refract) when moving through layers of air of different temperatures- example: Dog barking at night – further away

- During the day the layer of air close to the ground is warmer than higher up- Since sound travels faster in warm air, it is refracted upwards- At night, the air closer to the ground is colder, while the air higher up is warmer- The sound waves are refracted towards the ground

Resonance- Resonance takes place when a system starts vibrating at it’s natural frequency as a result of the impulse received from another source that is vibrating at the same frequency http://www.youtube.com/watch?v=hiHOqMOJTH4

http://www.youtube.com/watch?v=17tqXgvCN0E

http://www.youtube.com/watch?v=j-zczJXSxnw&feature=related

Factors influencing the speed of sound1) Elasticity

- This factor explains the difference in the speed of sound in the three phases- Elasticity is the ability of a material to keep it’s shape and not change when a force is applied to it- 3 phases: Solids > liquids > gases- For particles that are held more strongly together (solids), the restoring force that causes the particle to move back to it’s original position is stronger (thus creating faster compressions and rarefactions)

2) Inertia- Only explained for gasses and liquids- heavier particles react slower to disturbances than lighter particles- thus, if all other factors are equal, sound travels faster through less dense media

3) Temperature- sound travels faster through media at higher temperature- The particles of the medium move faster at higher temperatures and can therefore carry the disturbance quicker

2

1nL

n

L2

The physics of musical instruments - Recall the concept of a standing wave…

- Patterns can only be formed at particular frequencies (harmonics / overtones)

- Length of the medium important (integral number ½ wavelengths)

or where: n = 1, 2, 3, 4…

- Stringed instruments - When the string is played or plucked, a transverse wave is formed that travels along it and is reflected at its ends - The waves traveling back and forward along the string interfere in such a way as to form a standing wave pattern - The simplest pattern is called the fundamental frequency (single antinode in the middle with a node ate each end). When a string is plucked this frequency will produce the dominant sound

http://www.youtube.com/watch?v=_S7-PDF6Vzc&feature=related

- If the string is made shorter and then played, it can vibrate to form the second harmonic. The wavelength is half that of the fundamental frequency and therefore twice the frequency of the fundamental. It is therefore a higher pitch - Whenever a note is sounded by a stringed instrument, it is a mixture of the fundamental together with the different harmonics. This combination gives the sound quality (tone)

- Wind instruments

- When we blow into an instrument, our lips (or the reed) start small vibrations. The vibrations that match the natural frequency of the air column are picked out and are magnified by resonance - The frequency of the fundamental depends on the length of the air column. This is adjusted by opening and closing holes along the length of the instrument (clarinet) or by extending the air column (trombone)

- Air columns - In a tube that is closed at one end and open at the other… - Air molecules that cause the vibration cannot vibrate at the closed end, so they are reflected back (resulting in a zero amplitude at the closed end - NODE) - At the open end, the particles are able to vibrate at their maximum amplitude (resulting in the formation of an ANTI-NODE) - Therefore, for the fundamental frequency, the length of the tube must be equal to a quarter of a wavelength…

http://www.youtube.com/watch?v=ynqzeIYA7Iw&feature=fvw

- In a tube where BOTH ends are open - the pattern for the fundamental frequency will consist of ANTI-NODES at both ends (maximum displacement of particles possible) and a NODE in the middle of the tube…

- It is interesting to note that, even though the standing wave pattern formed in a pipe open at both ends, doesn’t look like the pattern formed on a string, that the values of the wavelengths and the harmonics are the same. Can you explain it?!