Question

the graphs below give information for waves w and x. both waves were produced in the same medium and are moving at the same speed.
which of the following statements describes a property of these waves? select two correct answers.
wave x has a lower frequency than wave w.
wave w has a lower frequency than wave x.
wave w has a shorter wavelength than wave x.
wave x has a greater amplitude than wave w.
wave x has a shorter wavelength than wave w.

Explanation:

Step1: Determine wavelength

Wavelength is the distance between two consecutive crests (or troughs). For wave \(W\), from \(0\) to \(20\) cm there are \(3\) wavelengths. So one wavelength \(\lambda_{W}=\frac{20}{3}\approx6.67\) cm. For wave \(X\), from \(0\) to \(20\) cm there is \(1\) wavelength. So \(\lambda_{X} = 20\) cm. So \( \lambda_{W}<\lambda_{X}\).

Step2: Use the wave - speed formula

The wave - speed formula is \(v = f\lambda\), where \(v\) is the speed of the wave, \(f\) is the frequency and \(\lambda\) is the wavelength. Since \(v_{W}=v_{X}\) (given), \(f=\frac{v}{\lambda}\). As \(\lambda_{W}<\lambda_{X}\), \(f_{W}>f_{X}\) (because \(v\) is constant).

Step3: Determine amplitude

Amplitude is the maximum displacement from the equilibrium position. For wave \(W\), the amplitude \(A_{W}=2\) m. For wave \(X\), the amplitude \(A_{X}=2\) m. So \(A_{W} = A_{X}\)

Answer:

Wave X has a lower frequency than Wave W. Wave W has a shorter wavelength than Wave X.