Chap 16

Waves

Sound (Continued)

Intensity of Sound in dB

  • The intensity of sound is commonly measured in decibels (dB).

Doppler Effect

Definition and Basic Concept

  • The Doppler effect refers to the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source.

  • When a source of sound is moving toward an observer:

    • The sound appears to have a higher frequency.

    • The wavelength appears to be shorter.

  • Conversely, when a source is moving away from the observer:

    • The sound appears to have a lower frequency.

    • The wavelength appears to be longer.

  • Source: Giancoli, Pearson, 4th Edition

Relationship Between Wavelength and Frequency

  • If the change in the wavelength is determined, then the change in frequency can also be determined.

Change in Frequency (Mathematical Representation)

  • For an observer:

    • If the source is moving away from the observer, the frequency is given by:

    • Formula: f' = f rac{v}{v + v_s}

    • Where:

      • f' = observed frequency

      • f = emitted frequency

      • v = speed of sound in the medium

      • v_s = speed of the source relative to the observer

Observer Moving Relative to Source

  • If the observer is moving with respect to a stationary source:

    • The wavelength remains the same, but the wave speed perceivable by the observer changes due to relative velocity.

Observers Moving Toward or Away from a Stationary Source

  • For an observer moving toward a stationary source:

    • The frequency observed increases:

    • Formula: f' = f rac{v + v_o}{v}

    • Where:

      • v_o = speed of the observer.

  • For an observer moving away from a stationary source:

    • The frequency observed decreases:

    • Formula: f' = f rac{v - v_o}{v}

Combined Equation for Doppler Effect

  • All four equations for the Doppler effect can be combined into a single unified equation, if the signs of the variables are tracked properly during calculations.

Doppler Ultrasonography

  • Doppler ultrasonography utilizes the Doppler effect to visualize movement, such as blood flow in vessels.

  • The frequency shift of blood flow relative to the ultrasound probe allows for the determination and visualization of:

    • The speed and direction of blood flow.

  • Color Doppler Imaging:

    • Velocity is displayed using a color scale, where color indicates the direction and speed of flow.

    • Typically combined with grayscale images to produce duplex ultrasonography, offering simultaneous anatomical visualization alongside blood flow information.

Red-Shift and Expansion of the Universe

  • The red-shift phenomenon is an implication of the Doppler effect observed in the context of the universe’s expansion.

    • Starlight moving toward Earth appears bluish (indicating a blue shift).

    • Starlight moving away from Earth appears reddish (indicating a red shift).

  • Observations show that all galaxies outside of our own exhibit a red shift, suggesting they are moving away from us.

Interference of Sound Waves; Beats

Interference of Sound Waves

  • Sound waves can interfere in a manner similar to other types of waves in a medium.

  • Interference can be constructive (amplitudes add) or destructive (amplitudes subtract).

Beats

Definition and Concept

  • Beats occur as a result of interference between two sound waves that have slightly different frequencies.

  • This phenomenon produces a slow varying perceived sound or “envelope” that outlines the resulting waveform.

Mathematical Representation of Beats

  • If two waves of the same amplitude and phase but different frequencies are considered, the beat frequency can be determined by:

    • Formula to find beat frequency: f{beat} = |f1 - f_2|

    • Where:

    • f{1} and f{2} are the frequencies of the two waves.

  • This results in a new wave oscillating at the average frequency, with an envelope defined by the difference of the two frequencies.

Summary

  • Vibrating objects serve as the primary sources of waves, which can be categorized as:

    • Pulses

    • Continuous waves

  • Waves can also be classified as:

    • Longitudinal

    • Transverse

    • Or both types simultaneously.

  • Characteristics of Simple Harmonic Motion:

    • Sinusoidal in nature.

    • The restoring force is proportional to the displacement from the equilibrium position.

    • Total energy oscillates between kinetic and potential forms, maintaining a constant total energy.

    • The period of the wave is independent of amplitude.

  • Wave Interference:

    • When two waves occupy the same space, they can interfere constructively or destructively.

  • Standing Waves:

    • Can be established on a string fixed at both ends.

    • Nodes occur at points of no motion, while antinodes occur at regions of maximum amplitude.

  • Physical properties of sound:

    • The pitch of a sound is primarily determined by its frequency.

    • Loudness relates to the intensity of sound, which is proportional to the square of the amplitude and also influenced by ear sensitivity.

  • The Doppler effect is characterized by frequency shifts resulting from the motion of either the source or the observer.

  • The frequency of beats is dictated by the difference in frequencies of two interfering sound waves.

Copyright Note

  • Content derived from Pearson Education, Inc., 2009.