PHYS112 : Homework Assignments

Homework Assignment 2 (due Sunday 2/1)

Mechanical Waves, Sound, and the Doppler Effect

Goals :

• Describe sinusoidal waves mathematically, and learn the associated vocabulary, including displacement $y$, amplitude $X$, wavelength $\lambda$, wave number $k$, frequency $f$, angular frequency $\omega$, initial phase $\phi_o$, and wave speed $v = \lambda f$.
  
  $$y(x,t) = Y \sin[(kx \pm \omega t) + \phi_o]$$
  
  

• Relate the intensity of a spherical wave to the power of its source.
  
  $$I = \frac{P}{4\pi r^2}$$
  
  

• Express the intensity of a sound wave in decibels.
  
  $$\beta [\mathrm{dB}] = 10 \log \left( \frac{I}{I_o} \right)$$
  
  

• Understand and apply the concepts of constructive and destructive interference, beats, standing waves, and resonance.

• Describe standing sound waves in cylindrical cavities, specifically, in a tube open at both ends
  
  $$f = n \left( \frac{v}{2 L} \right) \hspace*{0.2 in} (n = 1,2,3 \ldots)$$
  
  
  or at one end
  
  $$f = (2n + 1) \left( \frac{v}{4 L} \right) \hspace*{0.2 in} (n = 0,1,2 \ldots)$$
  
  

• Calculate the Doppler shift in the frequency of a moving source of sound waves. (The top sign in the numerator (denominator) is applied if the observer (source) is moving toward the source (observer). )
  
  $$f' = \left( \frac{ v^\mathrm{air} \pm v_D} { v^\mathrm{air} \mp v_S} \right) f$$
  
  

Your assignment is posted on the UT Homework Service (Class no. 99940)

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Updated Mon Mar 30 10:17:29 2009