A harmonic wave is traveling along a rope. It is observed that the oscillator that gener- ates the wave completes 38.9 in 27.4 s. Also, a given maximum travels 432 cm along the rope in 10.6 s.

What is the wavelength? Answer in units of cm.

To calculate the wavelength of the harmonic wave, we need to use the formula:

Wave speed = wavelength × frequency

Here's how you can find the wavelength step by step:

1. Calculate the frequency of the wave using the given information that the oscillator completes 38.9 oscillations in 27.4 seconds.
Frequency = Number of oscillations / Time taken
Frequency = 38.9 / 27.4

2. Calculate the wave speed by dividing the distance traveled by the given maximum (432 cm) by the time taken (10.6 s).
Wave speed = Distance / Time
Wave speed = 432 / 10.6

3. Now, rearrange the formula to solve for wavelength:
Wavelength = Wave speed / Frequency

4. Substitute the calculated wave speed and frequency into the equation to find the wavelength.

Finally, calculate the wavelength by dividing the wave speed (step 2) by the frequency (step 1).

Therefore, the wavelength of the harmonic wave is the result obtained after dividing the wave speed by the frequency.