A harmonic wave is traveling along a rope. The oscillator that generates the wave completes 40.0

vibrations in 30.0 s. A given crest of the wave travels 425 cm along the rope in a period of 10.0 s.What is the wavelength? Show all of your work plz.

i know the answer is 0.319 m but needs the stps of finding it plz

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

wavelength = speed / frequency

The speed of the wave can be determined by dividing the distance traveled by the time taken:

speed = distance / time

In this case, the distance traveled by a given crest is given as 425 cm, and the time taken is 10.0 s. Let's convert the distance to meters for consistency:

distance = 425 cm = 425 / 100 = 4.25 m

Next, we need to calculate the frequency of the wave. Frequency is defined as the number of complete vibrations or cycles per unit time. The number of vibrations completed by the oscillator is given as 40.0 in 30.0 s. Therefore, we can calculate the frequency as follows:

frequency = number of vibrations / time

frequency = 40.0 / 30.0 = 1.33 Hz

Now that we have the speed (4.25 m) and the frequency (1.33 Hz), we can substitute these values into the wavelength formula:

wavelength = speed / frequency

wavelength = 4.25 m / 1.33 Hz = 3.19 m

The wavelength of the harmonic wave is 0.319 m (rounded to three decimal places).