Final answer:
The wavelength of a harmonic wave can be calculated using the speed of the wave and its frequency, which in this case results in a wavelength of 1.66 meters.
Step-by-step explanation:
To calculate the wavelength of a harmonic wave traveling along a rope, we consider the frequency and the speed of the wave. The number of waves that pass a point per unit time is called the frequency, and the distance a wave travels per unit time is the wave speed.
In the given question, it is stated that 20 complete waves pass every 25 seconds, which gives us the frequency (f) after doing the appropriate calculation (f = number of waves/time). To find the frequency, you would divide 20 waves by 25 seconds, resulting in 0.80 Hz. The speed (v) of the wave is given as 8.0 m in 6.0 seconds, which we again calculate by dividing distance by time, giving us (8.0 m / 6.0 s = 1.33 m/s).
The wavelength (λ) can then be calculated using the formula λ = v / f. Plugging in the values for v and f, we get λ = 1.33 m/s / 0.80 Hz = 1.66 meters (rounded off to two decimal places).
So, the wavelength of the wave is 1.66 meters.