Waves

Waves

Transverse and longitudinal waves

Transverse waves

Transverse waves are made up of vibrations or oscillations that are at right angles (perpendicular) to the direction of motion of the waves. Vibrations are simply a repeating pattern, in the case of transverse waves it is the up and down motion as shown in the diagram below.

Examples of transverse waves are water waves and waves in the electromagnetic spectrum such as radio waves.

water waves

Longitudinal waves

Longitudinal waves are waves in which the oscillations are in the same plane or parallel to the direction of motion of the waves. Examples of longitudinal waves are sound waves and some types of waves that cause earthquakes.

Notice on the diagram above areas of high pressure called compressions where the particles are close together and areas of low pressure called rarefactions where the particles are further apart.

Vibrations produced by a speaker produces sound waves which are in the range of human hearing between 20 Hz to 20,000 Hz.

Exercise 1

1. Describe how the vibrations differ, relative to motion, in waves called:

a) Transverse waves

b) Longitudinal waves

2. State one example for each type of the following waves:

a) Transverse

b) Longitudinal

Properties of waves

Waves are made up of vibrations which are repeating cycles. The length of one complete cycle is called a wavelength. Waves have peaks called crests and the distance between any two consecutive crests is a wavelength (symbol λ). The amplitude is a measure of the intensity of a wave and is the distance from the baseline or equilibrium position to the top of a crest as shown in the diagram below. The frequency (symbol f) is the number of waves passing a point each second and so can be defined as the number of cycles per second.

The time taken to complete a wavelength is called the period. The formula that links period T and the frequency f is:

T = 1/f

T = period (s) where s is the time in seconds

f = frequency (Hz) where Hz is the unit called Hertz which is the number of cycles per second

Exercise 2

1. Calculate the period of a wave having a frequency of 200 Hz.

2. Calculate the period of a wave with a frequency of 25 KHz.

3. Calculate the frequency of a wave with a period of 2 s.

4. Calculate the frequency of a wave with a period of 50 ms.

5. Look at the diagram below and state which letter represents the:

a) crest

b) amplitude

c) wavelength

6. Using the diagram below determine the frequency of the wave.

All waves follow obey the equation that links wave speed v, frequency f and wavelength λ.

v = fλ

here v = speed in m/s

f = frequency in Hz

λ = wavelength in m

All units are SI units and any multiples or sub-multiples should first be converted to standard SI units before calculation is carried out.

Exercise 3

For the following calculations use the wave speed as:

here v = speed in m/s

f = frequency in Hz

λ = wavelength in m

1. Calculate the wavelength of a radio wave with a frequency of 2 MHz.

2. Calculate the frequency of a light wave with a wavelength of 300 nm.

3. Calculate the frequency of a light wave with a wavelength of 700 nm.

4. What colour do the following wavelengths of visible light produce:

a) 300 nm

b) 700 nm

Electromagnetic waves

Electromagnetic waves are a group of waves that belong to the electromagnetic spectrum and are made up of changing electric and magnetic fields. They are all transverse waves so that they vibrate or oscillate at right angles to the propagation of the wave. They all have the following properties:

they travel at the same speed which is the speed of light 300,000,000 m/s
they are all transverse waves
they can travel through a vacuum
they are made up of changing electric and magnetic fields which are at right angles to each other

Types of electromagnetic waves

As the frequency of the electromagnetic waves increases the wavelength decreases by a corresponding amount so that the wave speed remains the same. This pattern of increasing frequency is observed going down the list in the table starting from radiowaves. As the frequency increases so does the energy and penetrating power of the wave so that at the bottom of the list gamma rays have the highest energy.

Exercise 4

1. In the diagram below fill in the missing electromagnetic waves arranged in order of increasing wavelength:

2. State four properties of electromagnetic waves.

Reflection

When a ray of light is reflected from a mirror the angle of incidence is equal to the angle of reflection. Note that a normal is a line perpendicular to a surface and should be included in ray diagrams. The angle of incidence and angle of reflection can be described as follows:

the angle of incidence is the angle between the incident ray and the normal to the surface of the mirror
the angle of reflection is the angle between the reflected ray and the normal to the surface of the mirror

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