# Properties of Waves

## Wave Progression

**Properties of Waves**

Amplitude: The height of a wave from its midpoint to the crest. (m)

Wavelength: Distance between two crests of the wave. (m)

Frequency: The number of waves per second passing a fixed point. (Hertz Hz)

Period: The time for one full wavelength to pass a fixed point. It is the inverse of frequency. (seconds)

Wave velocity: The speed of the wave (m/s)

_velocity = frequency x wavelength expressed as v = f__λ__ _

_λ__ is pronounced Lambda _

Wavefront: A series of imaginary lines representing the position of similar points in the wave at any given point in time. Normally this is the position of the crests of the wave.

Example: Five waves break onto a beach every 10 seconds, what is the frequency of the wave?

Frequency = number of waves / time = 5 / 10 = 0.5 Hz

What is the velocity of this wave if each wave is 5 m apart?

_v = f__λ__ = 0.5 x 5 = 2.5 m/s _

When a wave travels forwards, (wave propagation) the material that carries the wave, such as the water, moves up and down, but not forwards. Only the wave and the energy it carries move forwards.

Try this: Find a small length of string or something similar: Hold one end firmly and move the other end up and down to produce a simple wave. You will observe the string does not move forward, it moved vertically - it is the wave that travels.

Think about this: Ever seen a Mexican wave (or been in one), the people stand up and sit down but they do not move around the stadium, only the wave does.

Sound waves: When you listen to music the wave passes through the air from the speaker to your ear. The information is carried to you by the wave, but the air does not move towards you if it did you would constantly feel a wind on your face.

## Types of Wave

Transverse waves: A wave in which the displacement of the material is at 90° to the direction of movement of the wave.

Examples include Electromagnetic Waves including light, s-waves in earthquakes and water waves.

Longitudinal Waves: A wave in which the displacement (vibration) of the material is in the same direction as the movement of the wave. Examples include sound waves and p-waves in earthquakes.

**Earthquakes**

During an earthquake, there are at least two types of waves making the ground move.

S-Waves (Shear waves) - These make the ground move up and down. If they are large enough they can do this to the ocean floor, creating massive waves called a Tsunami. S-waves are transverse waves, so are tsunami waves.

P-Waves: These waves make the earth jolt backwards and forwards, they shake objects. The earth is moving forwards and backwards in the same direction as the wave so it is a longitudinal wave.

## Calculating Wave Speed

The speed or velocity of a wave can be calculated in two ways.

*Velocity = frequency x wavelength v = fλ*

or

*Velocity = distance travelled by wave front / time taken v = x / t*

Example: Earthquake

An earthquake occurs 20 Km from a town, the inhabitants notice a jolting side to side movement 4 seconds after the earthquake occurred. Then 6 seconds later the ground moved up and down. What was the velocity of the two waves?

P-Waves arrived after 4 seconds over a distance of 20Km which is 20,000m

*v = x / t* = 20,000 / 4 = 5000 *m/s or 5 Km/s*

The S-wave arrived after 10 seconds.

*v = x / t _ = 20,000 /10 = 2000 _m/s or 2 Km/s*

A seismometer at the town recorded 22 vibrations in the 6 seconds between the p and s waves. What was the wavelength of the p-waves?

_Frequency = Number of wave / time _ 22 / 6 = 3.67 Hz

_v = fλ so λ = v/ f _5000 / 3.67 = 1362.4 m

## Measuring Wave Speed

**Water waves:** e.g ripples in a pond.

Method A: Measure the distance between each crest of the wave and then count how many waves arrived at the pond’s edge over a set period of time, like 10 seconds.

Divide the number of waves by the time to get the frequency and then use, *v = fλ*

Method B: Time a single wave as it travels from the epicentre of the ripples to the edge of the pond. Measure the distance and use , *v = x / t* .

**Sound Waves:**

Unlike water waves, you cannot see the waves so taking direct measurements is not possible.

Method A: Two people stand at either end of a football field (or similar), one has the means to produce a loud noise with a visual clue to the production of the sound. A starter pistol used in athletics works well. The second person has a stopwatch. When the pistol is fired the observer will see the smoke instantly and starts the stopwatch, when they hear the sound they stop the watch and record the time. Using _v = x / t _the speed of the sound wave can now be calculated.

Method B: If two microphones are placed apart and connected to a computer display that can show the sound wave, the time between each microphone detecting the sound can be measured. Using *v =x /t* , the velocity can be calculated.

Method C: The echo method. In this simple exercise, a sound is generated and directed at a wall or other reflective surface, the time taken for the echo to come back to the observer is divided by two and the velocity can be measured.

If your method and calculations are done correctly the answer will be around 343 m/s, but it does vary with air temperature.

- Describe the difference between a transverse and a longitudinal wave.
- Your answer should include: motion / 90 / same / direction

Explanation:*The motion of the material is at 90° to the wave for transverse waves but in the same direction as the wave in the case of the longitudinal wave* - A ripple on a pond takes 3 seconds to travel 2 m across the pond. What is the velocity of the wave?
- Your answer should include: 0.67m/s / 0.67

Explanation:*velocity = distance / time = 2 /3 = 0.67 m/s*