1. Vibrations and Sound Chapter 17

2. Sound travels as a wave, so it exhibits reflection, refraction, diffraction and interference. We hear sound due to the compression of air molecules – because air is the medium of sound humans are used too but it also travels through solids and liquids.

3. Sound waves related to transverse air pressure displacement

4. Speed of sound in air at 0 o C is approximately 330 m s -1 Above Thrust SSC and the shockwave produced

5. Frequencies which are multiplies of a certain frequency are called overtones of that frequency. If f is a given frequency: 2f is its 1 st overtone, 3f is its 2 nd overtone … etc.

6. The loudness of a sound wave depends on the amplitude of the sound wave. The greater the amplitude, the greater the loudness. The pitch of a note depends on the frequency of the sound wave. The higher the frequency the higher the pitch, the lower the frequency the lower the pitch. The quality of a musical note depends on the number of overtones present in the note and the relative strengths of the different overtones. Beats are also used in music…

7. The frequency limits of audibility are the highest and lowest frequencies that can be heard by a normal human ear. The range is approximately 20Hz – 20000Hz. Click here for generator…Click here for generator…

8. If the frequency of a periodic force is applied to a body is the same as or very near to its natural frequency that body will vibrate with very large amplitude, this is called resonance. Some examples of resonance include : –Barton’s pendulums –Rattling in cars at various speeds, rattling in water pipes when water flows at a particular rate. –The “singing” wine glass – see demo… –Chinese Spouting Bowl – see demo…

9. Another example of resonance Chinese Spouting bowl

10. One of the most dramatic examples of resonance was the Tacoma Narrows Bridge collapse in the summer of 1940.

11. Tacoma Narrows Bridge Collapse The bridge was to link Gig Harbour to Tacoma in Washington State (northwest America).

12. Left: the first bridge opened in July 1940. See it’s fate in November 1940 here…See it’s fate in November 1940 here… Above right is the current bridge built in the 1950’s.

14. A second “new” Tacoma Narrows Bridge Under construction March 2006 Completed CG bridge (above left ). Completion date Spring 2007.

15. The sound intensity (I) at a point is the rate at which sound energy is passing through unit area at right angles to the direction, in which the sound is travelling at that point, i.e., The units are watts per metre squared, W m -2.

16. Sound levels give us an idea of how different sounds compare. Exposure to very loud sound can damage hearing so protection for ears should be used. The dB(A) scale is used as it’s adapted to human ears.

18. Doubling the sound intensity increases the sound intensity level by 3.

19. A string vibrating with an antinode at its centre and a node at each end (and no other nodes or antinodes) is vibrating at its fundamental frequency. Fundamental frequency of a string is inversely proportional to its length i.e. This setup is known as a standing wave. See next slide for diagram.

20. Standing waves on a string fixed at both ends

22. Harmonics Frequencies which are multiplies of a certain frequency f are called harmonics. F is called the fundamental frequency or the first harmonic. If f is the first harmonic; 2f is the second harmonic; 3f is the third, etc.

24. If ‘T’ is the tension in the string, μ is its mass per unit length, l is its length and f its fundamental frequency of vibration then: T and μ are fixed. l and μ are fixed. T and l are fixed. It follows that: where k is a constant.

25. It can be proved that k = ½, giving:

26. Harmonics in a pipe closed at one end.

28. Figure 1 Figure 2 In figure 1: Thus In figure 2: Thus

29. Similarly, f 3 =5f 1

30. Stationary waves produced in a pipe open at both ends

32. Frequency = f Frequency = 2 f Frequency = 3 f Above would include examples such as tin whistles.