Question

each graph, the horizontal axis shows the horizontal position of particles of the rope, measured from where maya stood. the vertical axis shows the vertical displacement of the rope, measured from the equilibrium position, at a specific moment in time. assuming the waves are traveling at the same speed, compare the waves. the amplitude is the wavelength is the frequency is

Explanation:

Step1: Amplitude

Amplitude is the maximum displacement from the equilibrium position. For Wave 1, the maximum displacement is \(1.5\) (from \(y = 0\) to \(y=1.5\)), for Wave 2, the maximum displacement is \(1\) (from \(y = 0\) to \(y = 1\)). So amplitude is greater for Wave 1.

Step2: Wavelength

Wavelength (\(\lambda\)) is the distance between two consecutive crests (or troughs). For Wave 1, from \(x = 2\) to \(x=12\) is one full - wave cycle (\(\lambda_1=10\) units). For Wave 2, from \(x = 2\) to \(x = 5\) is a half - wave cycle, so \(\lambda_2 = 6\) units. So wavelength is greater for Wave 1.

Step3: Frequency

The formula for wave speed is \(v=\lambda f\), where \(v\) is speed, \(\lambda\) is wavelength and \(f\) is frequency. Given \(v_1 = v_2\) (same speed). Since \(v=\lambda f\), then \(f=\frac{v}{\lambda}\). Since \(\lambda_1>\lambda_2\), then \(f_1

Answer:

	greater for Wave 1	greater for Wave 2	equal for both waves
The wavelength is	\(\checkmark\)
The frequency is		\(\checkmark\)