The mechanical wave model

Learn.

The mechanical wave model describes a transfer of energy through a medium. This means a mechanical wave can not be transferred through a vacuum, for this reason most movies which play sound effects of explosions in space are not realistic since the sound would not actually be able to move through the vacuum of space. It is important to remember the medium doesn’t move with the wave but the particles within the medium move like the mexican wave where the people stay still but there hands go up in the air.

This model is represented with the following equation.

v = f λ

The velocity (v) (m/s) in this equation describes the speed the wave is travelling (as well as its direction). Think of this as how fast a surfer is travelling when they are riding a wave if they were just travelling perpendicular to the wave.

The frequency (f) (Hz or S^-1) is a measure of how many waves pass within a given time frame. For the surfer waiting to catch a wave, it would be the number of waves that would pass him in 1 second.

The wave length (λ) (m) is the length of a wave from crest to crest or trough to trough, this would be the distance between waves for a surfer measured in meters.

There are two types of mechanical waves:

  • Transverse waves

This is when the particles in the medium move perpendicular to the direction of propagation. So if a wave is moving from left to right, then the particles are moving up and down.

An example of this is the waves you see with a skipping rope is you shake it up and down.

  • Longitudinal waves

This is when the particles are moving in the direction of propagation. This means if the wave is moving from left to right then the particles are also moving from left to right.

An example of this is sound waves. Sound propagates through air, it can be diagrammatically represented by the following.

The waves you see at the beach are a combination of these two waves and are called surface waves where the water particles move around in a circle as opposed to either moving up or down or backwards and forwards.

Another way to describe a wave is using the period (T). This is a measure of how long it takes a single wave to pass by. Which is given by the reciprocal of the frequency

T = 1/f

In order to describe the loudness of a wave, the amplitude is required. The louder a wave the larger the amplitude. The amplitude is the half the maximum displacement of a particle, measured in meters. For the surfer riding the wave this would be the size of the wave. This is also the height of either the crest or the peak from the centre.

Memorise.

The wave model v = fλ describes both: 

  • Transverse waves

Particles move perpendicular to direction of propagation e.g. skipping rope wave

  • Longitudinal waves

Particles move parallel to direction of propagation e.g. sound wave

  • Velocity (m/s) = speed of the wave
  • Frequency (Hz or s^-1) = number of waves a second
  • Wavelength (m) = distance from peak to peak 

Amplitude (A) (m) is the size of displacement of the particles which is half the total displacement.


Master.

Problem 1:

A sound wave is a mechanical wave. What type of wave is it and what does this mean?

a. Transverse wave so the particles in the medium move perpendicular to the direction of energy transport.

b. Longitudinal wave so the particles in the medium move perpendicular to the direction of energy transport.

c. Transverse wave so the particles in the medium move parallel to the direction of energy transport.

d. Longitudinal wave so the particles in the medium move parallel to the direction of energy transport.

Problem 2:

Which of the following is not a characteristic of mechanical waves?

a. They consist of perpegations or oscillations within a medium.

b. They transport energy.

c. They travel in a direction that is at parallel to the direction of the particles of the medium.

d. They are created by an oscillating source.

Problem 3:

A film plays an explosion in space which makes a nearby star ship move and the people within the ship hear the sound. Explain why/ why not this would have occurred.

Problem 4:

Fisherman want to create there own sonar device for fishing which will tell them if there are fish beneath them and where the bottom of the boat is. Would you expect sonar to be a longitudinal or a transverse wave?

The wave equation

Problem 5:

The wave has a frequency of 4 Hz and a wavelength of 20 m, what is the velocity of the transverse wave?

Problem 6:

The wave has a period of 10 seconds and a wavelength of 20 m, what is the velocity of the transverse wave?


Challenge

Problem 7:

The wave has a velocity of 6 m/s and a wavelength of .20 km, what is the period of the transverse wave?


Answers

%d bloggers like this: