Lecture 20: Sound Practice Flashcards

Fundamentals of Sound Waves

• Definition of Sound: Sound waves are defined as vibrations consisting of increasing and decreasing pressure that propagate through some type of medium.

• Medium Requirements: Because sound waves are caused by pressure disturbances, they specifically require a medium to travel. These media can be solids, liquids, or gases.

• Broad Applications: Sound is of high interest in various fields, including:

  • Audio and music applications.

  • Studying how sound causes objects to resonate and leads to the amplification of energy.

• Longitudinal Nature: Sound waves are classified as longitudinal waves, which are generated by changes in air pressure between two specific points.

• Mechanism of Sound Production (The Speaker Demo):

  • Speakers function by converting electrical signals into physical vibrations.

  • A demonstration involved placing small pieces of paper on a speaker membrane. When the sound source is activated, the membrane vibrates back and forth, moving the paper.

  • Frequency Control: The frequency of the sound source determines how quickly the vibrations occur. At lower frequencies, the physical movement of the paper is easily observable.

Perception of Sound: Pitch and Loudness

• Pitch and Frequency:

  • The frequency of a sound wave directly controls the perceived pitch.

  • Increasing the frequency of the sound wave results in a higher audible pitch.

  • Pressure vs. Time Graph: When viewed through a microphone and software, higher frequencies show oscillations that occur more frequently within a given timeframe.

• Loudness and Amplitude:

  • The amplitude of a sound wave is proportional to its loudness or volume.

  • If the frequency is held constant while the amplitude is increased, the volume heard will increase.

  • Pressure vs. Time Graph: In the graph, the frequency of oscillation remains constant, but the vertical displacement (amplitude) increases as the sound becomes louder.

Musical Instruments and Hearing

• Creation of Sound in Instruments: Different instruments generate sound waves via various vibration methods:

  • Strings: Vibrating a physical string (e.g., guitar).

  • Wind/Reed: Blowing air across a reed or mouthpiece (e.g., tuba, piccolo).

  • Membranes: Creating vibrations on a stretched surface (e.g., drum).

• Timbre: The quality or "color" of a sound wave is known as timbre. This property is determined by the materials, design, and overall quality of the specific instrument.

• Size and Pitch Relationship:

  • Large instruments, such as the tuba or bass violin, support standing waves with large wavelengths ($\lambda$). Because of the inverse relationship between wavelength and frequency, these large instruments produce sounds with low frequencies.

  • Small instruments, such as the piccolo or kazoo, support standing waves with small wavelengths ($\lambda$). Consequently, they produce sound waves with high frequencies.

  • General Rule: Large instruments create low-pitch sounds, while small instruments create high-pitch sounds.

• Human Hearing Range:

  • The average human ear is capable of hearing sounds within the range of approximately $20\,\text{Hz}$ to $20,000\,\text{Hz}$.

  • Individual Variability: This range varies by person and changes with age. Starting around the age of $30\,\text{years}$, the upper range of hearing begins to degrade.

  • Age Effect: Older individuals possess a lower frequency limit for their upper range of hearing. A high-pitched noise audible and bothersome to a young person may be completely silent to an older adult.

Ultrasonic and Infrasonic Sound

• Ultrasonic Waves: Sound waves with frequencies exceeding $20,000\,\text{Hz}$ are classified as ultrasonic.

  • Application 1 (Motion Detectors): Motion sensors use ultrasonic waves that reflect off a nearby surface and return to the detector to calculate distance.

  • Application 2 (Medicine): Ultrasound is frequently used for medical diagnostics and imaging.

• Infrasonic Waves: Sound waves with frequencies below $20\,\text{Hz}$ are classified as infrasonic.

  • Natural Sources: Phenomena such as earthquakes, volcanoes, and waterfalls emit infrasound.

  • Monitoring: Infrasound detectors are used to monitor and study these natural events.

The Speed of Sound

• Medium Dependency: The speed at which pressure vibrations travel is entirely dependent on the medium.

• Molecular Interaction: Sound travels when molecules bump into one another to transmit energy.

• Phase of Matter:

  • Solids: Sound travels fastest through solids because the molecules are tightly packed, allowing for rapid energy transfer.

  • Liquids: The speed is slower than in solids but faster than in gases.

  • Gases: Sound travels slowest in gases because molecules are far apart.

  • Vacuum: Sound waves cannot travel through a vacuum at all because there are no molecules to create pressure vibrations.

• Speed of Sound in Air:

  • The primary factor influencing speed in air is temperature ($T$). Humidity and wind speed also have minor effects.

  • The Equation: The experimentally derived formula for the speed of sound ($v$) in air relative to temperature in degrees Celsius ($T$) is:       $v = 331\,\text{m/s} + 0.6 \times T$

  • Room Temperature Calculation: At a room temperature of approximately $20\,^\circ\text{C}$, the speed is:       $331\,\text{m/s} + 0.6 \times 20 = 343\,\text{m/s}$

• Light vs. Sound: Speed of light is significantly faster than the speed of sound ($343\,\text{m/s}$). This leads to synchronicity issues when observing distant events.

  • Example: A person watching a basketball player dribble from a distance will see the ball hit the ground before they hear the sound of the bounce. This effect increases with distance.

• Independence of Wave Properties: The speed of sound does not depend on the frequency or amplitude of the sound wave. Speaking louder or at a higher pitch does not change how quickly the sound travels.

Reflection, Refraction, and Interference

• Reflection:

  • Definition: Reflection occurs when waves bounce off a surface.

  • Echoes: A reflection is called an echo when it bounces off a distant surface, causing a perceptible delay between the initial sound and the reflected wave.

  • Distance Measurement: By knowing the speed of sound (calculated via temperature) and the time for a wave to return to a sensor, the formula $v = \frac{d}{t}$ is used to determine distance.

• Refraction:

  • Definition: Refraction is the bending of waves that occurs when the speed of sound changes, such as when traveling through significant temperature differences.

• Interference:

  • Acoustic Interference: Sound waves can interfere constructively or destructively. In concert halls, this can cause the resonance to sound unusual at specific seating locations.

  • Concert Hall Design: To prevent unwanted interference, acoustic spaces use strangely shaped panels to randomly reflect sound waves.

The Phenomenon of Beats

• Definition: Beats are produced when two sound waves of very similar (but not identical) frequencies interfere with each other.

• Auditory Quality: The result is a single musical tone with a fluctuating amplitude that sounds like a repetitive "WAH WAH WAH."

• Beat Frequency Calculation: The frequency of the beat ($f_{\text{beat}}$) is the absolute value of the difference between the two source frequencies ($f_1$ and $f_2$):   $f_{\text{beat}} = |f_1 - f_2|$

• Numerical Example:

  • Source 1: $480\,\text{Hz}$

  • Source 2: $489\,\text{Hz}$

  • Calculation: $|489\,\text{Hz} - 480\,\text{Hz}| = 9\,\text{Hz}$

• Verification via Period:

  • On a graph, two subsequent crests of a beat occurred at $0.13\,\text{s}$ and $0.02\,\text{s}$.

  • Period ($T$): $0.13\,\text{s} - 0.02\,\text{s} = 0.11\,\text{s}$

  • Frequency ($f$): $f = \frac{1}{T} = \frac{1}{0.11\,\text{s}} \approx 9\,\text{Hz}$

Forced Vibration and Resonance

• Forced Vibration:

  • Occurs when one vibrating object causes another object to vibrate at the same frequency.

  • Example 1 (Tuning Fork): Striking a tuning fork with a mallet makes it vibrate. If placed in a beaker of water, the water splashes, visually showing the stored energy.

  • Example 2 (Table): A vibrating tuning fork placed on a table forces the table to vibrate at that same frequency.

  • Example 3 (Guitar): Plucking a string forces the body of the guitar to vibrate.

• Natural Frequency: The specific frequency at which an object tends to oscillate based on its unique size and shape.

• Resonance:

  • Definition: Resonance occurs when an object is forced to vibrate at its own natural frequency.

  • Result: This leads to an amplification of energy.

  • Example 1 (Swing Set): A person pumping their legs at the natural frequency of the swing increases the amplitude of the motion.

  • Example 2 (Connected Pendulums Demo): Two identical pendulums are connected to a tube along with pendulums of different lengths. Swinging the first pendulum sends vibrations through the tube. Only the identical pendulum on the other side (sharing the same natural frequency) will begin to oscillate significantly; the others do not move.

  • Standing Waves: Resonance can also occur in systems like vocal cords, musical instrument cavities, or blowing across a glass bottle.

• Resonance in Other Fields:

  • Lasers use optical resonance for coherent light beams.

  • Electric circuits use resonance for tuning radio or television stations.

• Dangers of Resonance: If energy amplification is not controlled, objects may break. Bridges or structures can collapse if they vibrate at their resonant frequency. Engineers must account for this in the design of buildings, airplanes, and bridges.