Properties of Waves

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

What is a wave? 

A wave is made up of periodic motion. Periodic motion is motion repeated at regular intervals. 

For example, a pendulum moving from left to right and back again is said to be periodic. One such complete motion, from one position to the other and back is known as an oscillation or a vibration. These are key words in describing periodic motion. 

The source of any wave is a vibration or oscillation. 

3.2 describe longitudinal and transverse waves in ropes, springs and water where appropriate

Waves move up and down, but energy moves forward. 

Waves move back and forth but energy moves forward. 

Transverse waves are waves that travel in a direction perpendicular to the direction of vibration. 

To clarify this: The waves on ropes are transverse when you move the rope up and down. The direction of wave motion is forward, to the opposite end of the rope. But the wave crest and trough are moving up and down, which is the direction of vibration as you are moving the rope up and down, which is perpendicular to the direction of wave motion-which is forwards. (Perpendicular-at right angles to)

Eg. Water and light waves are transverse waves. 

Longitudinal waves are waves that travel in a direction parallel to the direction of vibration. 

If you were to push and pull a spring so that it compresses and expands, you would notice that when the coils move forward and backwards, the direction of the wave motion is parallel to the direction of vibration. It is moving along the spring, left and right, in the same direction that you are pushing/pulling it, not up and down like a transverse wave. 

E.g. sound waves are longitudinal waves. 

3.3 state the meaning of amplitude, frequency, wavelength and period of a wave

Amplitude (A): This is the maximum displacement from the rest/centre position. It is the height of the crest or depth of a trough measured from the rest position. It tells you the 'loudness' if it's a sound wave. The bigger the amplitude, the louder the sound. Its SI unit is the metre (m). 

Frequency (f): This is the number of complete wave produced per second. SI unit-hertz (Hz). Frequency relates to the pitch of a sound, the higher the frequency the higher the pitch. 

Period (T): This is the time taken for one point on the wave to complete one oscillation. Or you can think of it as the time taken to produce one complete wave. The SI unit is second (s). 

Wavelength (λ): The shortest distance between a point on one wave and the same point on the next wave. (in fancy words: the shortest distance between any two points in a wave that are in phase) such as two successive crests or troughs. 

For longitudinal waves, it is the distance between two successive compressions or rarefactions. Its SI unit is the metre (m). 

3.4 recall that waves transfer energy and information without transferring matter

A wave transfers energy and information from one place to another without transferring matter in the process. For example, when we drop a pebble into a pond, a few circular ripples move outward on the surface of the water. As the ripples spread outward, any object on the surface of the water (e.g. a leaf) would only bob up and down, not moved. This shows that waves transfer energy without transferring any matter! (The leaf bobs up and down because water waves are transverse.)

Another example: you can produce waves on a rope by fixing one end to a wall and moving the other end up and down. These up-and-down movements produce vibrations, or oscillations. Observe: the rope waves travel towards the wall, while the rope itself only moves up and down. The top is said to be the medium through which the waves move, or propogate. (This may also clarify a bit about transverse waves...) Waves transfer energy, not matter. The kinetic energy from the up-and-down movement is transferred by the wave from one end to the other. The rope itself, however, does not move from one end to the other. 

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

wave speed=frequency x wavelength

v= f x  λ 

3.6 use the relationship between frequency and time period:

frequency= 1/time period

f= 1/ T

So a higher frequency implies that more waves are produced in one second. This means that the period T will be shorter. 

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

Question: A wave is introduced into a thin wire held tight at each end. It has an amplitude of 3.8 cm, a frequency of 50 Hz and a distance from a crest to the neighbouring trough of 12.8 cm. Determine the period of such a wave.

Answer: f=1/T, so T=1/f

The question had a lot of useless information to throw you off, all you have to do is use T=1/f, so T=1/50

T=0.02s

Question: 

1. Some ripples travel 55cm in 5 seconds. Find their speed in cm/s.
2. The wavelength of these waves is found to be 2.2cm. What is their frequency?

Answer: 

1. 55/5=11cm/s
2. v= f x  λ  so f=v/ λ (use the equation triangle I included above) f=11/2.2=5Hz

Question: What is the wavelength of a sound wave of frequency 100 Hz. (speed of sound=340 m/s). 

Answer: 

v= f x  λ 

λ= v / f 

λ= 340 / 100 = 3.4m