When a bell is rung, standing waves are set up around the bell’s circumference. What boundary conditions must be satisfied by the resonant wavelengths? How does a crack in the bell, such as in the Liberty Bell, affect the satisfying of the boundary conditions and the sound emanating from the bell? Two speakers are driven in phase by a common oscillator at 800 Hz and face each other at a distance of 1.25 m. Locate the points along a line joining the two speakers where relative minima of sound pressure amplitude would be expected. (Use v =343 m/s.) An airplane mechanic notices that the sound from a twin engine aircraft rapidly varies in loudness when both engines are running. What could be causing this variation from loud to soft?
Answers
louder amplitude louder sounds...lower amplitude lower sound
(i) Boundary conditions are divided into two categories: fixed-endpoint or Dirichlet boundary conditions and free-endpoint or Neumann boundary conditions, which equate to keeping the end of a string or letting it to freely oscillation. Standing waves can result from any sort of boundary condition, in which some sites called nodes have zero displacement at all times and the maximum amplitude of the wave at all points remains constant over time.
(iii) The facing speakers produce a standing wave between them. The spacing between the nodes is λ/2 = v/2*f = 3432 × 800 m = 0.214 m ; If the speakers vibrate in phase, the point nidway between the speakers will be an antinode and the distance of the antinode from either speaker is 0.25² =0.625m ; There is a node at one quarter of wavelengh at 0.625 m.
(iv) The vibrations from the two engines from the twin engine aircraft must emit sound waves that are in phase or undergoing additive superimposition leading to a higher amplitude of sound and hence loud sound is produced.