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 time period of 10.0 s. What is the wavelength?

frequency=40/30 hz

wave velocity= 4.25m/10 sec

frequency*wavelength=wavevelocity
calculate velocity

0.425 Wavelenth = velocity / frequecy

Frequency=40vibration / 30s=1.33HZ
425cm *100 = 4.25m
Then divide 4.25 m by 10 (the period)
4.35/10 = 0.425 m
(I am sorry for the previous answer my bad)

It has a wavelength of 0.319m

0.141525

0.78352941

4.2 meter

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

wavelength = speed / frequency

First, we need to find the speed of the wave. The speed of a wave traveling along a rope can be calculated using the formula:

speed = distance / time

In this case, we are given that a given crest of the wave travels 425 cm in a time period of 10.0 s. Therefore, the distance is 425 cm and the time is 10.0 s.

speed = 425 cm / 10.0 s = 42.5 cm/s

Next, we need to find the frequency of the wave. The frequency is the number of vibrations or oscillations per second. In this case, we are given that the oscillator completes 40.0 vibrations in 30.0 s.

frequency = number of vibrations / time

frequency = 40.0 vibrations / 30.0 s = 1.33 vibrations/s

Finally, we can substitute the values of speed and frequency into the wavelength formula to find the wavelength:

wavelength = speed / frequency

wavelength = 42.5 cm/s / 1.33 vibrations/s ≈ 31.95 cm

Therefore, the wavelength of the harmonic wave is approximately 31.95 cm.

Wavelenth = velocity / frequecy

Frequency=40vibration / 30s=1.33HZ
425cm *100 = 4.25m
Then divide 4.25 m by 1.33
4.35/1.33= 3.19m then divide by 10
3.19/10 = 0.319
(I am sorry for the previous answer my bad)