5. An air column 2 ft. long closed at one end is resonant to what wave length? What number of vibrations will this sound have per second at 25°C.? 6. At 24°C. What length of air column closed at one end will be resonant to a sound having 27 vibrations a second? 7. A given note has 300 vibrations a second. What will be the number of vibrations of its (a) octave, (b) fifth, (c) sixth, (d) major third? 8. In the violin or guitar what takes the place of the sounding board of the piano? 9. Can you explain why the pitch of the bell on a locomotive rises as you rapidly approach it and falls as you recede from it? 10. Do notes of high or low pitch travel faster? Explain. 11. An "A" tuning fork on the "international" scale makes 435 vibrations per second. What is the length of the sound waves produced? (5) WAVE INTERFERENCE, BEATS, VIBRATION OF STRINGS =340. Interference of waves.=--The possibility of two trains of waves combining so as to produce a reduced motion or a _complete destruction_ of motion may be shown graphically. Suppose two trains of waves of equal wave length and amplitude as in Fig. 329 meet in _opposite phases_. That is, the parts corresponding to the _crests_ of _A_ coincide with the _troughs_ of _B_, also the troughs of _A_ with the crests of _B_; when this condition obtains, the result is that shown at _C_, the union of the two waves resulting in complete destruction of motion. _The more or less complete destruction of one train of waves by another similar train is an illustration of_ =interference=. If two sets of water waves so unite as to entirely destroy each other the result is a level water surface. If two trains of sound waves combine they may so interfere that silence results. The conditions for securing interference of sound waves may readily be secured by using a tuning fork and a resonating air column. If the tuning fork is set vibrating and placed over the open end of the resonating air column (see Fig. 328), an increase in the sound through resonance may be heard. If the fork is rotated about its axis, in some positions no sound is heard while in other positions the sound is strongly reinforced. Similar effects may be perceived by holding a vibrating fork near the ear and slowly rotating as before. In some positions interference results while in other positions the sound is plainly heard. The explanation of interference may be made clear by the use of a diagram. (See Fig. 330.) Let us imagine that we are looking at the two square ends of a tuning fork. When the fork is vibrating the two prongs approach each other and then recede. As they approach, a condensation is produced at 2 and rarefactions at 1 and 3. As they separate, a rarefaction is produced at 2 and condensations at 1 and 3. Now along the lines at which the simultaneously produced rarefactions and condensations meet there is more or less complete interference. (See Fig. 331.) These positions have been indicated by dotted lines extending