PHYS122

Doppler Effect

• The general Doppler formula for sound:Vs = Speed of sound, V₂ = Speed of listener, fs = Frequency of source

  • From the listener toward the source is +

  • Positive direction noted in the formula:

    • Formula: ( f' = f \frac{(V + V_s)}{(V + V_2)} )

Example of Doppler Effect

• A car drives at 30 m/s honking a horn at 300 Hz.

  • Sound reflects off a building.

  • The driver hears the frequency: 358 Hz

Wavelength Changes

• Movement of source alters wavelength.

  • Waves behind a moving source are stretched.

  • As the source moves away, wavelength increases.

Shock Waves

• Occur when an object exceeds the speed of sound.

  • Creates compressions in air, resulting in a shock wave.

• Relevant formula: ( \sin \alpha = \frac{
  u}{
  u_s} )

  • Where ( v ) is the speed of sound, ( v_s ) is the speed of source.

Speed of Sound

• Wave speed is independent of the source speed.

  • Dependent on medium's compressibility and density.

  • Compressibility correlates to elastic modulus.

Characteristics in Different Mediums

• Fluid (water) sound speed is different from solids (rods).

• For gases (air) speed of sound is influenced by:

  • Temperature, density, and elasticity of the gas.

Speed of Sound in Air

• Relationship with temperature:

  • At 0°C, speed = 331 m/s

  • At 20°C, speed = 343 m/s

  • Formula: ( v = 331 + 0.6 \cdot T ) (temperature in °C)

Energy, Power, Intensity

• Power formula:[ Power = \frac{Energy}{time} ]

• Intensity formula:[ Intensity = \frac{Power}{Surface Area} ]

Sound Intensity Level

• Measured in decibels (dB).

  • 0 dB is the threshold of human hearing.

  • Sound intensity levels:

    • Safe at 70 dB.

    • Painful at 120 dB.

    • Reference intensity I₀ at 1000 Hz.

Concept of Charge

• In electrostatics, only two types of charge exist: positive & negative.

Electric Force Laws

• Charge interactions governed by Coulomb’s law:

  • Like charges repel, opposite charges attract.

Electric Charge Properties

• Materials can be either conductors or insulators.

  • Insulators restrict charge flow; conductors permit it easily.

• Charged objects can exert forces on neutral objects:

  • Example: Charged balloon sticks to an uncharged wall.

Conductors vs. Insulators

• Conductors allow free movement of electric charges, insulators do not.

Charging by Induction

• Creating charge without contact:

  • Bringing a charged object close induces charge redistribution.

Coulomb's Law

• The electrostatic force between two charged objects varies inversely with the square of the distance between their centers.

Force Direction

• Determined by charge interactions:

  • Like charges: repeal.

  • Opposite charges: attract.

Electric Fields

• Electric fields represent the force a charge experiences due to other charges.

  • Direction of the field is in the direction of force on a positive charge.

Summary of Electric Field Concepts

• Electric forces exert influence by creating fields in space.

  • A test charge experiences the electric field produced by other charges.