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 ( $f_d$ ):
- $fd = fs * (v - vd) / (v - vs)$
- 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.