Sound and Doppler Effect

Question 1

Speed of Sound in Solid, Liquid, and Gas

Speed of Longitudinal Wave in Gaseous Media

Answer 1

• Sound propogates through a solid at a greater rate than a liquid and gas
  
  • The stronger the force between any two molecules, the greater the restoring force between those molecules
  • The faster molecules are restored, the faster they propogate, aka, faster speed
• v = ((γRT)/(M))^1/2

Question 2

Pitch

Answer 2

• The pitch regards the frequency of a sound
  
  • High pitch means higher frequency while low pitch refers to a lower frequency
• Frequency of sound is directly proportional to pitch

Question 3

Intensity

Intensity Formula

Answer 3

• Intensity regards the loudness of a sound
  
  • Higher intensity means loud and lower intensity means soft
• Amplitude of wave is directionaly proportional to intensity
• Intensity = (energy)/(area x time) = (power)/(area) = P/A
  
  • Recall, (energy/time) = power
  • W/m²

Question 4

Decible

Answer 4

• We can compare the intensity of a sound with the intensity of a reference sound
• β = (10)log(I/I₀) = the intensity level, in units decible (dB)
• Decibles measure log increases of intensity
  
  • So, from 0 dB to 10 dB, there has been a 10 fold increase in intensity
  • From 0 dB to 20 dB, there has been a 100 fold increase in intensity
  • From 0 dB to 30 dB, there has been a 1000 fold increase in intensity, etc.

Question 5

Doppler Effect

Answer 5

• There is a chnage in the intensity of the sound with distance, as well as a perceived change in the frequency (pitch) of the sound. The change in pitch of a sound from a high frequency as it approaches an observer to a low frequency as it moves way from the observer. This is called the doppler effect.

Question 6

Doppler Effect Equation

Answer 6

• f_L = ((v + v_L)/(v))f_s
  
  • _​When the listener (L) moves towards a source (S), the observed frequency increases; when the L moves away from an S, the observed frequnecy decreases
• f_L = ((v)/(v - v_s))f_s​
  
  • When the S moves towards the L, the observed frequency increases; when the S moves away from the L, the observed frequency decreases

Question 7

Fundamental Frequency

Answer 7

• The fundamental frequency is the first harmonic in a series of related waves
• f₁ = v/(2L)
• λ₁ = 2L

Question 8

Harmonics

Answer 8

• Harmonics refer to the frequencies that are integer multiples of the fundamental frequency, f₁
• f_n = nf₁
• λ_n = (λ_n)/n

Question 9

Open Pipes

Answer 9

• Open pipes can vibrate at all multiples of the fundamental frequency
• f_n = (nv)/(2L)
  
  • f = v/(2L)
  • λ = 2L; L = λ/2

Question 10

Closed Pipe

Answer 10

• Closed pipes cannot vibrate at twice the fundamental frequency
• f_n = (nv)/(4L)
  
  • n = 1, 3, 5, …
  • f = v/(4L)
  • λ = 4L; L = λ/4