13. What is the wavelength of a sound wave that has a period of .05 seconds, and a speed of \( 343 \mathrm{~m} / \mathrm{s} \) ?

To find the wavelength, you can use the formula: \[ \text{Wavelength} = \text{Speed} \times \text{Period} \] However, since we often use frequency instead of period in these calculations, we need to find the frequency first. The frequency (\( f \)) is the inverse of the period (\( T \)): \[ f = \frac{1}{T} = \frac{1}{0.05} = 20 \text{ Hz} \] Now, using the speed of sound: \[ \text{Wavelength} = \frac{\text{Speed}}{f} = \frac{343 \mathrm{~m/s}}{20 \text{ Hz}} = 17.15 \text{ m} \] So, the wavelength of the sound wave is approximately 17.15 meters. This means that a sound wave that takes a full cycle of 0.05 seconds to complete travels about the length of an average bus in a single cycle! Isn’t that fascinating how sound waves can travel such distances through the air? And remember, the relationship between speed, frequency, and wavelength is fundamental to understanding sound waves, so keep it in mind the next time you're playing music or experiencing sounds!