Wave Dynamics Chapter 4. Sound Waves
Recommended Article : 【Physics】 Physics Table of Contents
4. Applications
1. Characteristics of Sound
⑴ Characteristic 1. Intensity or Amplitude : Loudness of sound
① Weber-Fechner law : Presents a scale for the intensity (sound pressure) of sound
② dB SPL (decibels sound pressure level)
○ Definition : Represents the magnitude of relative sound pressure on a logarithmic scale
○ dB SPL = 0.1 B SPL = 10 × log10(I / I0) = 20 × log10(P / Pref)
○ Pref = 0 dB SPL = 0.0002 dyne/cm2 = 20 μPa
③ dB HL (decibels hearing level)
○ Definition : Represents the sound intensity based on the average threshold of audibility (0 dB HL) for normal young adults (18-30 years old, male and female)
○ dB HL = 20 × log10(P1 / P2)
○ 0 dB HL ≒ 7 dB SPL (at 1 kHz)
○ Audiometric Zero = 0 dB HL at each frequency
④ dB SL (decibels sensation level)
○ Definition : Represents sound intensity greater than an individual’s threshold
○ Stimulus intensity - Threshold = sensation level
○ Example : A patient with a 30 dB loss perceives 50 dB SPL as 20 dB SL
⑵ Characteristic 2. Frequency (Pitch) : Highness or lowness of sound
② Audible Frequency : 16 ~ 20,000 Hz
③ Conversational Frequency : 250 ~ 2,000 Hz
④ Below 1,000 Hz : Distinguishable approximately every 1 Hz
⑤ Above 1,000 Hz : Distinguishable at more than 0.1% intervals of the reference frequency
⑥ Head Shadow Effect (Baffle Effect)
○ Definition : Phenomenon where higher-frequency sounds lose more energy than lower-frequency sounds as they pass over the head
○ The ear opposite to the sound source perceives lower sound
○ Brain integrates information from both ears to process frequency information
⑶ Characteristic 3. Phase : Temporal relationship between two simultaneous sounds
⑷ Characteristic 4. Spectrum, Tone, or Timbre
① Pure Tone : Tone represented by a single sine function
② Complex Tone : Tone represented by two or more sine functions
○ Musical Tone : Periodic, pleasant
○ Noise : Irregular, unpleasant
2. Speed of Sound
⑴ Formula : For density ρ (kg/m3) and bulk modulus B (N/m2)
⑵ Derivation
If the pressure acting on fluid element ρAΔx is P0 + p1 on the left and P0 + p2 on the right, the net force is
The equation of motion is
Dividing both sides by Δx and taking the limit,
Also, from the expression of bulk expansion,
The change in pressure ΔP has an average value of p1 or p2, which is p. Then
Substituting this equation into the equation of motion
Therefore, the speed of sound is as follows.
⑶ It can be expressed as follows
⑷ Speed of Sound in Liquid
① In liquids, isothermal change occurs
② Formulation
○ Tip: Sound speed decreases with increasing pressure
○ Tip: Inference can be easily made through dimensional analysis
③ (Note) Nozzles and Sound Speed
○ Purpose of Nozzle : Increase flow velocity. i.e., raise kinetic energy
○ Enlarging Nozzle : Supersonic possible
○ Constricting Nozzle : Subsonic possible
○ Nozzle Throat : Sound speed cannot be exceeded
⑸ Speed of Sound in Air
① In air, adiabatic change occurs
② Formulation
○ k : Specific heat ratio
○ R : 287 J/kg·K
③ Tip: Density has little effect, only temperature matters
○ Crows listen in the day, mice listen at night
○ Warm ground causes higher sound speed, leading to upward refraction
○ Cold ground causes slower sound speed, leading to downward refraction
⑹ Speed of Sound in Space
① Space was considered vacuum, thought sound cannot propagate
② In 2003, NASA demonstrated that sound can propagate in space
③ Thus, pressure waves generated by black holes vibrate interstellar gas, creating and propagating sound
3. Propagating Sound Waves
⑴ Expression of Sound Waves traveling through a Tube
① Displacement
② Pressure
③ When displacement is maximum, pressure change is 0, and when displacement is 0, pressure change is maximum
⑵ Relationship between Pressure Amplitude and Displacement Amplitude
4. Applications
⑴ Application 1. Bats
① Bats use reflected ultrasonic waves from prey to locate their position
② Bats use the Doppler effect to determine prey’s velocity
⑵ Application 2. Ultrasonic Testing
① 1st. Ultrasonic waves generated by the testing device
② 2nd. Ultrasonic waves reflected from blood
③ 3rd. Determine blood velocity using the frequency difference of the two ultrasonic waves → Assess patient’s health status
Figure. 1. Ultrasound Examination
⑶ Application 3. Structural Diagnostics (e.g., Crack Detection), Underwater Depth Measurement
⑷ Application 4. Shock Waves
① Definition : A sonic discontinuity generating a loud noise, irreversible, increases pressure, density, and entropy
② Related to the reinforcement interference of sound
③ Vertical shock waves lead to subsonic flow behind the shock
Input : 2019.05.03 17:46