Converting a wavelength to frequency helps us understand how often the wave oscillates per second. To achieve this, we use the formula: \[ f = \frac{v}{\lambda} \]where:
- \( f \) represents the frequency in hertz (Hz).
- \( v \) is the speed of sound in meters per second (m/s).
- \( \lambda \) is the wavelength in meters (m).
This formula is derived from the basic relationship between wavelength, frequency, and speed, which states that wave speed is the product of frequency and wavelength.
Let's apply this to our guitarists. The first guitar's wavelength is 64.8 cm, which is converted to meters as 0.648 m. Using a standard speed of sound (340 m/s), the frequency is calculated as \( f_1 = \frac{340}{0.648} \approx 524.69 \text{ Hz} \).
Similarly, the second guitar has a wavelength of 65.2 cm or 0.652 m, thus its frequency is calculated as \( f_2 = \frac{340}{0.652} \approx 521.38 \text{ Hz} \). Understanding this conversion is crucial for analyzing sound waves.