Waves and Sound

What is a Wave?

• A wave is a disturbance that travels through a medium.

• Waves transport energy from the source to another location without transporting matter.

• Two Types:

  • Longitudinal

  • Transverse

Wave Anatomy

• Peak or Crest

• Trough

• Wavelength or Period

  • Should be measured from peak to peak or from trough to trough.

  • Short wavelength means a high energy wave.

• Amplitude is the height of a wave.

  • Tall waves are considered more powerful waves.

Wave Frequency

• Wavelength:

  • Length of single wave pulse.

  • Typically measured in meters.

• Frequency:

  • How many waves pass per second.

  • Unit is Hertz or Hz.

  • Hertz means “things per second”.

  • 60 Hz wave = 60 waves per second

• Frequency is inversely proportional to Wavelength: f \propto \frac{1}{\lambda}

Wave Speed

• Speed is measured in meters/sec.

• Wavelength is in meters.

• Frequency is in Hz (or 1/sec).

• Meters * Hz = meters per second = m/s

• V = f \lambda

• Example:

  • Wavelength = 1 meter

  • Frequency = 1.5 Hz

  • Speed = 1.5 Hz * 1m = 1.5 m/s

Wave Energy & Power

The slide with Wave Energy and Power contains the equation:
P = \frac{64\pi}{pg^2} H^2 T m_o \Delta\Phi
This appears to be retracted in the following slide.

Reflections

• Closed end reflection:

  • Particle momentum is downward at the reflection point.

  • This causes reflection to be on the opposite side.

• Open End reflection:

  • Particle momentum is upward at the reflection point.

  • Reflection returns on the same side.

Superposition

• When multiple waves are in the same location, their heights combine until they completely pass one another.

• This is known as superposition and can cause wave interference.

Interference

• Constructive Interference

• Destructive Interference

Standing Waves

• Standing waves occur when a continuous wave reflects off a closed end and interferes with itself.

• Example: a jump rope or slinky tied to a fixed end and continuously wiggled back and forth at the energy source.

Standing Waves and Harmonies

• All closed ended wave mediums have natural frequencies or “harmonies”.

• Relationship between these frequencies and the length:

  • L = n\frac{\lambda}{2}

  • \lambda = \frac{2L}{n}

  • Where:

    • L = string length

    • \lambda = wavelength

    • n = number of Antinodes (Harmonic Value)

Oscillating Motion

• Describes repeating, back and forth motion

• Examples:

  • Pendulums

  • Mass on a spring

  • Circular Motion

  • Vibrating Strings

Pendulums

• A hanging mass that swings back and forth

• The frequency of motion relies on the length of the string only

  • Mass and angle have no effect on simple pendulums

• Energy transfer in a pendulum is shown below

Pendulums & Waves

• Why is \pi a part of the formula for the period of a pendulum swing?

Mass on a Spring

• Elastic force: F_e = -kx (“Hooke’s Law”)

• Potential energy stored in a spring: PE_s = \frac{1}{2}kx^2

• Kinetic Energy: KE = \frac{1}{2}mv^2

• Molecules are often thought of as masses attached by springs

Mass on a Spring & Waves

• The motion of a mass on a spring can also be described with waves

• The time period formula has \pi again.