How Do You Calculate the Wavelength of a Traveling Wave?

[djlightsout06]

A sinusoidal wave is travelingh along a rope. The oscillator that generates the wave completes 40.0 vibrations in 30.0s. Also, a given maximum travels 425cm along the rope in 10.0s. What is the wavelength?

 

[AKG]

The wavelength is (among other things) the distance traveled by a given maximum in one period (one cycle of oscillation). You can find the period given the numbers you have. The period is the time taken for 1 cycle/vibration.

T = 30.0s/40.0 vibrations = 0.750 seconds/vibration

$\lambda$
= distance travelled/cycle
= distance travelled/second * seconds/cycle
= 4.25m/10.0s * 0.750s/cycle
= 0.31875 m/cycle
= 0.319 m (you don't really have to say, "/cycle")

so the wavelength (notice that it's only good to 3 significant digits) is 31.9 cm.

 

[M98Ranger]

To solve this problem, we can use the formula for wavelength, which is λ = v/f, where v is the velocity of the wave and f is the frequency. In this case, we are given the frequency of the oscillator, which is 40.0 vibrations in 30.0s. To find the velocity, we can use the formula v = d/t, where d is the distance traveled and t is the time. We are given that the maximum travels 425cm in 10.0s, so the velocity would be 425cm/10.0s = 42.5 cm/s.

Now, we can plug in the values into the wavelength formula: λ = (42.5 cm/s)/(40.0 vibrations/30.0s) = 31.875 cm. Therefore, the wavelength of the wave is 31.875 cm.