A harmonic wave is traveling along a rope.

The oscillator that generates the wave com-
pletes 46.0 vibrations in 26.5 s. A given crest
of the wave travels 351 cm along the rope in a
time period of 12.5 s.
What is the wavelength?
Answer in units of m

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

wavelength = speed / frequency

First, let's find the speed of the wave.

The speed of a wave can be determined by multiplying the frequency (vibrations per second) with the wavelength.

In this case, the frequency can be calculated by dividing the number of vibrations completed by the time taken:

frequency = number of vibrations / time taken

Given that the oscillator completes 46.0 vibrations in 26.5 seconds, we can substitute the values into the formula:

frequency = 46.0 vibrations / 26.5 s

Next, let's determine the speed of the wave by multiplying the frequency with the given time period in which a crest travels a distance:

speed = frequency * distance

The distance given is 351 cm, which needs to be converted to meters:

distance = 351 cm * (1 m / 100 cm)

Now, let's substitute the values into the formula to calculate the speed:

speed = (46.0 vibrations / 26.5 s) * (351 cm * (1 m / 100 cm))

Finally, we can find the wavelength by dividing the speed by the frequency:

wavelength = speed / frequency

Substitute the calculated values into the formula:

wavelength = (speed) / (frequency)

Once you have the values for speed and frequency, divide speed by frequency to obtain the wavelength.

Remember to convert the wavelength to meters as requested in the answer.