Chapter Six, Seven and Eight Unit Three Waves and Sound Chapter Six, Seven and Eight

6.1 Vibrations Waves transfer energy over a distance in the form of a disturbance. This disturbance can be caused by the vibration of an object. A vibrating object has a ‘rest’ position and will periodically shift from this state to another. Think of the type of vibrational motion exhibited in the following examples.

A weight hanging from a rope and the rope is twisted. A weight hanging from a spring. A weight hanging from a rope and the rope is twisted. A pendulum. A piece of wood floating in the ocean. Periodic motion occurs when an object repeats a pattern of motion. The vibration, or oscillation is repeated over and over with the same time interval.

Types of Vibrations There are 3 basic types of vibrations: transverse vibrations, longitudinal vibrations, and torsional vibrations. A transverse vibration occurs when an object vibrates perpendicular to its axis at the normal rest position (such a pendulum). A longitudinal vibration occurs when an object travels parallel to its axis at the rest position.

axis movement axis movement

A torsional vibration occurs when an object twists around its axis at the rest position, for example a human twisting to the left or the right periodically. Observe the twist to the left, then the rest position, then the twist to the right.

One complete oscillation of a vibrating object is called a cycle One complete oscillation of a vibrating object is called a cycle. A cycle would be complete relative to a point in the object’s vibration. This is when the object travels past that point in the same direction. Possible cycles: 1,2,3,2,1 2,3,2,1,2 3,2,1,2,3 Not 2,3,2 !!!

The number of cycles which occur per second is called the frequency of vibration (f). Frequency is measured in hertz (Hz) or s-1. The period of vibration (T) is the time required to complete one cycle. Period is measured in seconds.

The distance in either direction from the equilibrium, or rest position to maximum displacement is called the amplitude (A) of vibration. A A A A

In phase In phase Out of phase Objects that are ‘in phase’ vibrate with the same period and pass through the rest position at the same time and in the same direction. In phase In phase Out of phase p. 198 1-8 p.202 1-11 Inertial Balance Activity

6.2 Wave Motion Waves transfer energy over a distance in the form of a disturbance. In transverse waves, particles in the medium move at right angles to the direction in which the wave travels. The high section of the wave is called the crest and the low section is a trough. The rest position is known as equilibrium. A wave that consists of a single disturbance is a pulse (may be positive or negative).

Periodic waves originate from periodic vibrations where the motions are continuous and repeated in the same time intervals. Wavelength (λ) Crest Amplitude Wavelength (λ) Trough

As the wave travels through any medium, its amplitude will decrease due to energy loss from friction. If no energy were required to overcome friction, an ‘ideal wave’ would be present. Demonstrate pulses, waves, reflections, reflection transmission, speed of medium then change, superposition.

Longitudinal waves In longitudinal waves, particles vibrate parallel to the direction of motion of the wave. The most common longitudinal waves are sound waves. In a longitudinal wave, regions where the particles are closer together than normal are known as compressions and the regions where they are farther apart than normal are known as rarefactions.

The amplitude will be the change in a physical quantity from the rest position to a maximum compression or minimum rarefaction. For sound this quantity would be air pressure. Wavelength (λ) Compression Rarefaction Compression Rarefaction v Wavelength (λ) Homework: p.208 3,4

6.3 The Universal Wave Equation A wave travels one wavelength in one period of time. f = frequency l= wavelength The speed of a wave is a property of the medium it travels in.

Homework: p.211 1,2 p, 211 1-8 (hand in) The distance between successive crests in a series of water waves is 4.0m. The crests travel 9.0m in 4.5s. What is the frequency of the crests? Δd = 9.0m Δt = 4.5s λ = 4.0m f = ? Homework: p.211 1,2 p, 211 1-8 (hand in)

6.4 Transmission and Reflections of Waves A change in the medium in which a wave is traveling often results in a change of the speed of the wave. The frequency of the wave or disturbance will never change however the wavelength of the wave must change if the Universal Wave Equation is to be upheld. Changes to the speed of the wave will ensure proportional changes in the wavelength of the wave.

Waves behave in various ways when they are reflected Waves behave in various ways when they are reflected. When waves undergo fixed end reflection the pulse is inverted. If the reflection occurs from a free end then there is no inversion. In both fixed end and free end reflection there is no change in frequency or wavelength. There is also no change in the speed of the pulse since the medium is the same.

Inverted reflected pulse Fixed end Free end Reflected wave is not inverted

When a wave travels into a new medium partial reflection occurs When a wave travels into a new medium partial reflection occurs. Some of the energy of the wave is transferred through to the new medium, but some is also reflected back into the original medium. Of course, since the wave is traveling into a new medium there will be a change in its wavelength and speed. The loss of energy also means a decrease in amplitude for the wave.

(Less dense to more dense Medium) Fast to Slow Medium (Less dense to more dense Medium) The slow medium acts like a rigid obstacle, and the reflected wave is inverted. The transmitted wave is not inverted, travels with reduced speed and wavelength and has a diminished amplitude. Incident Pulse Fast Medium Slow Medium Reflected pulse Transmitted Pulse

(More dense to less dense Medium) Slow to Fast Medium (More dense to less dense Medium) The fast medium acts like a free end and the reflected wave is not inverted. The transmitted wave is not inverted, travels with increased speed and wavelength and has a diminished amplitude. Incident Pulse Fast Medium Slow Medium Reflected Pulse Transmitted pulse

6.6 Interference of Waves Wave interference occurs when two waves act simultaneously on the particles of a medium. There are two types of interference: constructive and destructive. Destructive interference occurs when a crest meets a trough. Constructive interference occurs when crests meet crests (supercrests) or troughs meet troughs (supertroughs).

Constructive Interference B Waves approach A A+B Waves occupy same space Waves diverge A B

Destructive Interference Waves approach A B Waves occupy same space A+B Waves diverge A B

This concept of adding the amplitudes of waves is known as the superposition principle. It states that at any point the resulting amplitude of two interfering waves is the algebraic sum of the displacements of the individual amplitudes. Homework: Superposition worksheet p. 222 1-3 (just sketch) Extra p. 221 1,2 p. 222 4,5

Waves approach each other Overlap Resulting Wave Pattern Remember this pattern only appears for an instant!

6.7 Mechanical Resonance Resonance is the response of an object that is free to vibrate to a periodic force with the same frequency as the natural frequency of the object. Therefore resonance is also a transfer of energy from one object to another having the same natural frequency. If the two objects are touching, it is known as mechanical resonance.

Every object has a natural frequency at which it will vibrate Every object has a natural frequency at which it will vibrate. A swing’s natural frequency will depend on the length of the chains. A window rattles with its natural frequency. Bridges, propellers, blades, turbines, glasses and many types of equipment all have a natural frequency. Read p. 223-224 for examples.

If you push someone on a swing at the right time they will travel higher and higher on a swing (with the swing’s natural frequency). Think what would happen if a bridge got “pushed” at the right time over and over . . . Tacoma narrows, singing rod, swing set, army marches When an object vibrates in resonance with another, it is called a sympathetic vibration.

6.8 Standing Waves – A Special Case of 1 Dimensional Wave Interference The amplitude and the wavelength of interfering waves are often different. However if the conditions are such that two waves have the same amplitude and wavelength and travel in opposite directions, then a special interference pattern known as a standing wave occurs. Try the standing wave worksheet.

The resulting wave pattern is known as the standing wave interference pattern. Node (N): point that remains at rest Antinode: point midway between nodes where maximum constructive interference occurs N N N N λ 2

The distance between two successive nodes in a vibrating string is 10cm. The frequency of the source is 30 Hz. What is the speed of the waves? f = 30 Hz λ = ? v = ? Distance between successive nodes is ½ λ ½ λ = 10 cm λ = 20 cm Hmwk. p.229 1-4 extra p.230 1-4 v = f λ v = (30 Hz)(0.20m) v = 6.0 m/s