Calculating Wavelength of a Harmonic Wave

[sun]

Homework Statement

A harmonic wave is traveling along a rope. It is observed that 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 wavelenght?

Homework Equations

v=f(lambda)

The Attempt at a Solution

My problem is understanding what 40.0 vibrations in 30.0s means. Is this a reference to the frequency? 40/30=1.3Hz?

 

[hage567]

Yes, that's the frequency.

 

[ogb p]

Assuming that 40.0 vibrations in 30.0s refers to the frequency of the wave, we can use the equation v=f(lambda) to solve for the wavelength. We know that the velocity of the wave (v) is equal to the distance traveled (425cm) divided by the time it takes (10.0s). So v=425cm/10.0s=42.5cm/s. We also know that the frequency (f) is equal to 1.3Hz. Therefore, we can rearrange the equation to solve for the wavelength (lambda):

lambda=v/f=42.5cm/s/1.3Hz=32.69cm

The wavelength of the harmonic wave is 32.69cm.