http://www.ck12.org Chapter 11. Vibrations and Sound
FIGURE 11.24
Illustrative Example 2
Resonance is established in a hollow tube similar to that shown inFigure11.24 with a tuning fork of 512 Hz. The
distance from the tube opening to the water level is 16.8 cm.
a. What is the velocity of sound according to this experiment?
Answer: The wave velocity equation isv=λf. One-fourth of the wave occupies the length of the tube for the first
harmonic. So the wavelength of the resonant wave must be four times the length of the hollow tube. That is,
λ 1 = 4 L= 4 × 16 .8 cm= 67 .2 cm= 0 .672 m
v= ( 0 .672 m)(512 Hz) =344 m/sb. The velocity of sound changes with temperature as given by the formulav= 330 + 0. 6 T, whereTis the tempera-
ture in degrees centigrade. Using the result of part A, determine the temperature at the location the experiment was
conducted.
Answer:We simply set the result of part A equal to the given equation:
344 = 330 + 0. 6 T→T= 23. 3 ◦C(or about 74◦F).