Waves Notes

Waves #1

Physics 11 AP

Waves

• Disturbances that travel through space, transferring energy.

• A model used to describe energy and its various properties (e.g., mechanical, light, sound, electromagnetic).

Types of Waves

• We can describe waves in two ways:

  • Travelling Waves

  • Standing (Continuous) Waves

Travelling Waves

• Waves that consist of a single, distinguishable disturbance transferring energy away from its source.

Standing / Continuous Waves

• Waves that originate from a source that produces a repetitive, periodic disturbance.

Properties of Waves

• Amplitude (A) – the vertical displacement of the disturbance.

• Wavelength ($\lambda$) – the distance between each disturbance.

Properties of Waves

• Frequency ($f$) – how many disturbances occur during a set amount of time (usually in cycles per second or Hz).

• Period (T) – the time it takes to complete one disturbance.

Types of Mechanical Waves

• Transverse Wave - the disturbance direction is perpendicular to the wave direction

  • Eg. ocean waves, electromagnetic waves.

• Longitudinal Wave - the disturbance direction is parallel to the wave direction

  • Eg. sound waves, spring waves.

Wave Velocity

• Wave velocity is constant.

• Using wave variables, knowing that $v = \frac{d}{t}$, $f = \frac{1}{T}$, and $v = \frac{\lambda}{T}$.

• We get the wave equation: $v = f\lambda$

Wave Velocity

• The velocity of a wave through a particular kind of material is dependent on its wavelength and frequency. However, as wavelength changes so will frequency, and thus, velocity will remain constant.

• Wave velocity only changes with a change in medium!

Wave Velocity

• If a wave was to move or transfer from one type of material to another then…

  • Velocity & Wavelength changes,

  • But Frequency REMAINS CONSTANT!

Wave Velocity Example

• The speed of light through air is $3.00 x 10^8$ m/s. What is the wavelength for an FM radio signal broadcast at 105.3 MHz?

• When the radio signal travels through a wall, the wavelength changes to 2.00 m. Calculate the new wave velocity.

Wave Dynamics

• a) Reflection

  • Fixed End: Reflection of wave at fixed end out of phase

  • Free End: Reflection of wave at free end in phase

Wave Dynamics

• b) Wave Interference / Interaction

  • Principle of Superposition when 2 or more waves meet, the resulting displacement is the algebraic sum of the individual separate wave displacements.

Wave Dynamics

• Constructive interference

• Destructive interference / cancellation

Wave Dynamics

• Meeting waves in phase

• Meeting waves out of phase

Wave Dynamics

• c) Standing Waves

  • If waves are frequently sent through a medium and reflected back, the incoming waves interfere with the reflected waves.

  • Constructive & destructive interference occur and standing waves are produced.

Wave Dynamics

• For a standing wave,

  • Points of destructive interference are called nodes

  • Points of constructive interference are called antinodes

Wave Dynamics

• If we increase the wave frequency, more waves will interfere with each other and thus more nodes and antinodes are produced.

Wave Dynamics

• d) Diffraction

  • When waves encounter a physical obstacle, such as a small opening, they bend and spread apart.

Wave Dynamics

• d) Diffraction

  • The amount of diffraction will increase when

    • the size of the opening decreases or

    • the wavelength of the wave passing thru the opening increases

Wave Dynamics

• d) Diffraction

  • When a single source of waves encounters two openings (or slits) diffraction occurs from both openings, and the waves interfere with each other.

Wave Dynamics

• d) Diffraction

  • Thus, constructive and destructive interference occur between waves after passing through the two slits.

Sound Waves

• Vibrating objects create disturbances that propagate through air molecules as longitudinal waves.

• Longitudinal waves consist of rarefactions and compressions.

Compressions and Rarefactions

• Compressions: Regions in a sound wave where air molecules experience maximum pressure.

• Rarefactions: Regions where air molecules experience minimum pressure.

• Speed of sound: $345 \text{ m/s}$

Visualizing Sound Waves

• Sound waves can be represented as transverse waves by plotting pressure vs. time.

• High pressure corresponds to points above the x-axis.

• Low pressure corresponds to points below the x-axis.

Volume and Amplitude

• Volume is directly proportional to the amplitude of the sound wave.

• Increase in volume implies an increase in amplitude.

• Frequency and wavelength remain constant when volume changes.

Pitch, Frequency, and Wavelength

• When pitch increases:

  • Frequency increases.

  • Wavelength decreases.

• When pitch decreases:

  • Frequency decreases.

  • Wavelength increases.

Audible Sound Waves

• Audible range: $20 \text{ Hz} - 20,000 \text{ Hz}$

• Infrasonic waves: Frequency less than $20 \text{ Hz}$

• Ultrasonic waves: Frequency greater than $20,000 \text{ Hz}$

Doppler Effect

• Doppler Effect: Compression and expansion of sound waves when the source of sound is moving.

• The pitch perceived by a listener in front of the source differs from the pitch perceived behind the source.