Mechanical Waves

Important Equations

f = # of cycles / second

 

f

 = Frequency 

T = # of seconds / cycle

 

 = Period

v

= Velocity (wave speed)

 

 = Wavelength 

Wave speed

   A wave is produced when a vibrating source periodically disturbs the first particle of a medium. This creates a wave pattern which begins to travel along the medium from particle to particle. The frequency at which each individual particle vibrates is equal to the frequency at which the the source vibrates. Similarly, the period of vibration of each individual particle in the medium is equal to the period of vibration of the source. In one period, the source is able to displace the first particle upwards from rest, back to rest, downwards from rest, and finally back to rest. This complete back-and-forth movement constitutes one complete wave cycle.

 Definition provided by Physics classroom

Important note

     Its important to note that the speed of a wave is not dependent on the frequency or the wavelength, instead it has more to do with the medium in which the wave travels through.  The relationship between wavelength frequency and speed goes more like this.  The frequency of a wave is typically one of the things in which we can control.  Because the wave is created in a particular substance which allows a wave speed regardless of the frequency. So because you created a wave with a certain frequency and because the wave was created in a certain medium (which has it own speed) then you end up with a wavelength that is shorted or longer depending on the frequency and speed.

     The reason this is important is Snell's law, that when light passes from one medium to another the frequency remains constant but the wavelength is free to change depending on the "speed" of light in that medium

What is a mechanical wave?

    A mechanical wave is a transfer of energy from one point in a medium to another by oscillations of the medium’s particles.  Previous methods of energy transfer involve using the kinetic energy of a mass. For example, a cannon shoots a projectile from one point to another. Chemical energy from the gun powder is converted into kinetic energy in the projectile. The projectile then moves through the air and carries with it the kinetic energy.  The energy is transferred to the target on impact.  In a mechanical wave, matter does not move far from its equilibrium position, energy is transferred from one particle in the medium to another via collisions or other forms of interactions.

Two types of mechanical waves

   There are 2 common types of mechanical waves that we will study, although many more exist, they are transverse waves, and longitudinal waves.  A slinky can be used to demonstrate these two types of waves.

    In transverse waves, the displacement of the particles in the medium are perpendicular to the direction of motion of the wave.  In the above applet, the waves created on the string move horizontally but the individual sections of the string move vertically.  Water waves are transverse waves because although the wave moves horizontally, the surface of the water only moves vertically.  A transverse wave can be seen at sports stadiums.  Spectators create a transverse wave in the audience by either standing up and sitting down one after the other, or by simply raisng and lowering their hands.

     Longitudinal waves are waves in which the particles in the medium move parallel to the direction of the wave.  The most notable longitudinal wave is a sound wave.  An initial displacement of the air particles cause each successive particle to be displaced as well.  This forces a wave of compressed particles to move through the medium.  A longitudinal wave can be created in a slinky by stretching it out, then pushing one end of the slinky in the direction it is stretched.

Definition provided by Physics Lab