Sound Waves Notes

Sound Waves

Nature of Sound Waves

• Sound waves are produced by vibrating sources (e.g., speakers).
• They are:
  • Longitudinal waves
  • Mechanical waves
  • Pressure waves
• When a string vibrates, it causes the molecules of gases in the air next to it to vibrate.
• The molecules squeeze together and then spread apart.

1- Longitudinal Waves

• The oscillations are along the same direction as the direction of travel and energy transfer.
• Direction of vibration is parallel to direction of travel.

2- Mechanical Waves

• Mechanical waves can only travel through a solid, liquid, or gas medium.
• In space or a vacuum, there are no particles to vibrate to produce sound.

3- Pressure Waves

• Due to the longitudinal motion of air particles, there are regions where air particles are compressed together (compressions) and regions where they are spread apart (rarefactions).
• Compressions are regions of high air pressure.
• Rarefactions are regions of low air pressure.

Sound Represented on a Pressure-Distance Graph

• Air pressure is highest at compressions and lowest at rarefactions.
• The representation of sound by a pressure wave illustrates pressure-time fluctuations.
• Sound is NOT a transverse wave with crests and troughs; it's a longitudinal wave with compressions and rarefactions.
• As sound passes through air, air particles do not vibrate in a transverse manner.

Wavelength

• Wavelength is the distance between two consecutive compressions OR the distance between two consecutive rarefactions.
• It is measured from one compression to the next adjacent compression or from one rarefaction to the next adjacent rarefaction.

Amplitude

• The deepest part of a trough or the highest part of a peak is called the amplitude.
• The amount of energy carried by a wave is related to its amplitude.
• A high-energy wave has a high amplitude; a low-energy wave has a low amplitude.
• Wave amplitude is determined by the energy of the disturbance that causes the wave.
• Large amplitude means a high-pressure reading (high density).
• Small amplitude means a lower-pressure reading (low density).
• The closer together the particles are, the greater the amplitude of the wave.

Properties of Sound - Amplitude

• The amplitude of a sound wave is related to the volume of the sound:
  • High amplitude sound waves are loud.
  • Low amplitude sound waves are quiet.

Decibel Scale

• Humans can detect sound waves of extremely low intensity.
• The scale for measuring intensity is the decibel scale.
• It's convenient to measure intensities on a logarithmic scale called the sound level.
• The most common unit of measurement for sound level is the decibel (dB).
• Sound level depends on the ratio of the intensity of a given sound wave to that of the most faintly heard sound.
• The faintest sound is measured at 0 dB.
• A sound that is ten times more intense registers 20 dB.
• A sound that is another ten times more intense is 40 dB.

Decibel Scale - Intensity Comparison

• The decibel scale is logarithmic, not linear.
• Every increase of 10 dB represents a sound that is 10 times more intense.
• Example: Difference between 40 dB and 80 dB
  • $80 - 40 = 40$ dB
  • Since each 10 dB = 10 times more intense, then a sound at 80 dB is $10^4 = 10,000$ times more intense than a sound at 40 dB.

Properties of Sound - Frequency

• The frequency of a sound wave is related to the pitch that is heard:
  • High-frequency sound waves are high-pitched.
  • Low-frequency sound waves are low-pitched.

Audible Range

• The human ear can detect fluctuations in air pressure that affect the eardrum.
• The human ear can detect sound waves with frequencies ranging from approximately 20 Hz to 20,000 Hz (20 kHz).
• Any sound with a frequency below 20 Hz is known as infrasound.
• Any sound with a frequency above 20,000 Hz is known as ultrasound.
• Bats can detect frequencies as high as 120,000 Hz.
• Dolphins can detect frequencies as high as 200,000 Hz.
• Elephants have an audible range from approximately 5 Hz to approximately 10,000 Hz.

Oscilloscope Traces

• Examples:
  1. Quiet, low-pitch sound
  2. Loud, low-pitch sound
  3. Loud, high-pitch sound

Waves Traveling Between Media

• When waves travel from one medium to another, the frequency never changes.
• The speed of the wave is directly proportional to the wavelength (when the speed increases, the wavelength increases).

Speed of Sound

• $speed = distance / time$
• The faster a sound wave travels, the more distance it will cover in the same period.
• Example: If a sound wave travels 700 meters in 2 seconds, then the speed is $350 m/s$.

Speed of Sound - Medium Properties

• The speed of any wave depends on the properties of the medium through which it is traveling, NOT on the frequency or the wavelength.
• In air, the speed of sound is about 330 meters per second (m/s).
• Sound cannot travel through a vacuum because there are no particles to carry vibrations.
• Sound travels faster in solids than in liquids or gases, as the speed depends on the density of the material.
• In water, sound travels at 1,400 m/s.
• In wood, sound travels at 4,000 m/s.
• In steel, sound travels at 5,790 m/s.

Speed Comparison

• V{solids} > V{liquids} > V_{gases}
• Steel: 5,941 m/s
• Water: 1,482 m/s
• Air: 343 m/s

The Doppler Effect

• When a stationary object emits waves, the waves spread out symmetrically.
• When the observer and the source are both stationary, the waves are at the same frequency for both.
• The Doppler effect is observed when the source of the sound waves is moving.
• To an observer standing in front of an object moving towards them, the waves appear to get squashed together (wavelength appears shorter, frequency appears higher).
• To an observer standing behind an object moving away from them, the waves appear to get stretched apart (wavelength appears longer, frequency appears lower).

Doppler Effect - Definition

• The change in the frequency of sound or light caused by the movement of either the source, the detector, or both.

Doppler Effect - Formula

• The frequency perceived by a detector ($f_d$):
  • $f<em>d = f</em>s * (v - v<em>d) / (v - v</em>s)$
  • Where:
    • $v$ = the velocity of the wave
    • $v_d$ = the velocity of the detector
    • $v_s$ = the velocity of the source
    • $f_s$ = the wave's frequency

Doppler Effect - Sign Convention

• Pay careful attention as to whether you need to use a + or - sign in the relevant equation!
• Label the 'observer' and 'source' on the exam paper.
• The positive direction is from the source to the detector.
  • Source moving toward the detector (positive direction).
  • Detector moving toward the source (negative direction).
  • Velocity of sound ($v$) is always positive.

Doppler Effect - Motion Direction

• Detector away from source: +
• Detector toward source: -
• Source away from detector: -
• Source toward detector: +

Doppler Effect - Scenarios

• Ambulance moves toward a person:
  • Detector: 0
  • Source: +
• Police car moves toward a standing person:
  • Detector: 0
  • Source: +
• Person walks toward a stationary siren:
  • Detector: -
  • Source: 0
• Person runs away from a stationary siren:
  • Detector: +
  • Source: 0
• Siren moves away from a person:
  • Detector: 0
  • Source: -
• Person and siren move toward each other:
  • Detector: -
  • Source: +
• Person and siren move away from each other:
  • Detector: +
  • Source: -

Applications of the Doppler Effect

• The Doppler effect occurs in all wave motion, both mechanical and electromagnetic.
• Radar detectors use the Doppler effect to measure the speed of baseballs and automobiles.

Radar

• Radar sends out waves (usually radio waves) toward a moving object, such as a car or a baseball.
• When these waves hit the moving object, they bounce back to the radar.
• The radar device measures the change in frequency and calculates the speed of the object.

Applications of the Doppler Effect - Astronomy

• Astronomers observe light from distant galaxies and use the Doppler effect to measure their speeds.

Astronomers and Distant Galaxies

• Light from galaxies changes color slightly depending on how they move.
• If a galaxy is moving away, its light shifts to red (called “redshift”).
• If it's coming closer, the light shifts to blue (called “blueshift”).
• Astronomers use this change in color to tell how fast galaxies are moving and in which direction.

Applications of the Doppler Effect - Medicine

• Physicians can detect the speed of the moving heart wall in a fetus using the Doppler effect in ultrasound.

Doctors and Ultrasound in Pregnancy

• Ultrasound sends sound waves into the body.
• These waves bounce off moving parts like the baby's heart.
• If the heart wall is moving toward or away, the sound waves change pitch slightly.
• The machine uses this change to measure how fast the heart is moving.