Page 747 - College Physics For AP Courses

Chapter 17 | Physics of Hearing 735
Figure 17.9 A sound wave emanates from a source vibrating at a frequency , propagates at , and has a wavelength .
Table 17.4 makes it apparent that the speed of sound varies greatly in different media. The speed of sound in a medium is determined by a combination of the medium’s rigidity (or compressibility in gases) and its density. The more rigid (or less compressible) the medium, the faster the speed of sound. This observation is analogous to the fact that the frequency of a simple harmonic motion is directly proportional to the stiffness of the oscillating object. The greater the density of a medium, the slower the speed of sound. This observation is analogous to the fact that the frequency of a simple harmonic motion is inversely proportional to the mass of the oscillating object. The speed of sound in air is low, because air is compressible. Because liquids and solids are relatively rigid and very difficult to compress, the speed of sound in such media is generally greater than in gases.
Applying the Science Practices: Bottle Music
When liquid is poured into a small-necked container like a soda bottle, it can make for a fun musical experience! Find a small-necked bottle and pour water into it. When you blow across the surface of the bottle, a musical pitch should be created. This pitch, which corresponds to the resonant frequency of the air remaining in the bottle, can be determined using Equation 17.1. Your task is to design an experiment and collect data to confirm this relationship between the frequency created by blowing into the bottle and the depth of air remaining.
1. Use the explanation above to design an experiment that will yield data on depth of air column and frequency of pitch. Use the data table below to record your data.
Table 17.1
2. Construct a graph using the information collected above. The graph should include all five data points and should display frequency on the dependent axis.
3. What type of relationship is displayed on your graph? (direct, inverse, quadratic, etc.)
4. Does your graph align with equation 17.1, given earlier in this section? Explain.
Note: For an explanation of why a frequency is created when you blow across a small-necked container, explore Section
17.5 later in this chapter.
Answer
1. As the depth of the air column increases, the frequency values must decrease. A sample set of data is displayed below.
Depth of air column (λ) Frequency of pitch generated (f)