AQA P1 5.1

5.1 Wave introduction

Waves transfer energy from one place to another. No matter is transferred (no solids, liquids or gases); only energy. Some waves must travel through a medium. For example, sound and seismic waves. Other waves do not need to travel through a medium and can travel through a vacuum. Electromagnetic radiation can travel through a vacuum.

We can work out the amplitude, wavelength and frequency of waves.

Amplitude: The amount of its disturbance from its undisturbed position. It is the distance between the rest point (the black centre line or X axis) and the crest). It is important to make sure that we are not measuring the distance between the crest and the trough as this will not work out the amplitude.
Wavelength: This is the length of a full cycle. It is the distance between the same point on a wave. It is easier to measure the wave length using a trough or a crest as during one wave length the wave only crosses it once. If you use a rest point on the wave you need to calculate the wave crossing the rest point twice (see video for explanation).
Frequency: This can be measured in two ways. It is the number of complete waves that pass through a certain point each second. Or it is the number of waves being produced by a source each second. Frequency is measured in hertz (Hz), and 1 Hz is one wave per second. If a wave has a very high frequency it can be measured in kilohertz (kHz), megahertz (MHz) or gigahertz (GHz). Radio stations broadcast radio waves with frequencies of about 100 MHz and wireless computer networks work at 2.4 GHz.

There are two types of waves; transverse waves and longitudinal waves.

With a transverse wave, the vibrations are perpendicular (right angle) to the direction of energy of the wave. So, if the direction of energy was to the right, the vibrations would be upwards and downwards. See the video for an example. Electromagnetic waves and ripples on water are examples of transverse waves.

Longitudinal waves have vibrations that are parallel to the direction of the wave. Let’s takes the example of a stretched spring. If you push the spring, the waves will move along the spring in the same direction as the spring is facing. Sound waves, ultrasound and shock waves (like seismic waves) are examples of longitudinal waves.

Wave Speed Equation
To work out the speed of a wave we use the formula below:

V = f x λ

Whereby:

V is velocity or wave speed measured in meters per second (m/s)
f is frequency in hertz (Hz)
λ is the wave length in meters (m)

The speed of a wave is related to its frequency and wave length. The higher both frequency and wave length, the faster the wave will be travelling.

Example 1
Suppose that we have a sound wave that has a frequency of 8,000 Hz and wave length of 0.041 m. What is its speed?

We know that to find a wave’s speed we use the formula below.
V = f x λ
We have values for the frequency (8,000 Hz) and wave length (0.041 m). Therefore, we multiple these values together to get 328 m/s.

Example 2
We have a radio wave with a speed of 250,000,000 m/s and a wave length of 90 m. What is the frequency of this wave?

By using the formula triangle, we can easily see that we work out the frequency by dividing the speed by the wave length. Thus, we divide 250,000,000 m/s by 90 m.

  f = V / λ
  f = 250,000,000 (m/s) / 90 m
  f = 2,777,777.78 Hz
  f = 2.78 MHz

Frequency & Time Period
A time period is the amount of time that it takes for one complete oscillation (i.e. the amount of time it takes for one wave length to occur). We can then work out the frequency by using the following formula:

f = 1 / T

Whereby:

f is frequency
T is time period

For example, it takes 0.000125 seconds for a sound wave oscillation, what is the frequency of this sound wave?

We use the formula above to give us:
  f = 1 / T
  f = 1 / 0.000125
  f = 8,000 Hz