A harmonic wave is traveling along a rope. The oscillator that generates the wave completes 40.0 vibrations in 27.0 s. A given maximum of the wave travels 455 cm along the rope in a time period of 10.0 s. What is the wavelength?
Use the wave equation
frequency*wavelength=velociyt
You are given the frequency (40/27) and velocity (4.55m/10s)
wavelength= .307m
To find the wavelength of a wave, you need to know the frequency of the wave and the speed at which it is traveling.
The frequency (f) of a wave is the number of vibrations or oscillations completed in one second. In this case, the oscillator completes 40.0 vibrations in 27.0 seconds. So, the frequency can be calculated as:
f = 40.0 vibrations / 27.0 s
To find the speed (v) of the wave, you can use the formula:
v = λ * f
where λ is the wavelength.
Given that a given maximum (also known as a crest or a trough) of the wave travels 455 cm in a time period of 10.0 seconds, we can calculate the speed of the wave as:
v = 455 cm / 10.0 s
Now, we can equate the two expressions for the speed and solve for the wavelength:
v = λ * f
455 cm / 10.0 s = λ * (40.0 vibrations / 27.0 s)
To isolate the wavelength (λ), we rearrange the equation:
λ = (455 cm / 10.0 s) * (27.0 s / 40.0 vibrations)
Now, plug in the given values and calculate:
λ = (455 cm / 10.0 s) * (27.0 s / 40.0 vibrations)