Figure 14.2 The figure shows a wave in a rope with two points labelled A and B.
-A harmonic wave travelling along the x-axis is described by the equation y(x, t) = (4 cm) sin[(0.5 cm) x - (1.05 s^-1) t) ]. What is the wavelength of the wave?

Question

Figure 14.2 Figure 14.2 The figure shows a wave in a rope with two points labelled A and B. -A harmonic wave travelling along the x-axis is described by the equation y(x, t) = (4 cm) sin[(0.5 cm) x - (1.05 s<sup>-1</sup>) t) ]. What is the wavelength of the wave? A) 0.5 cm B) 1.05 cm C) 4.0 cm D) 12.6 cm

Figure 14.2 The figure shows a wave in a rope with two points labelled A and B. -A harmonic wave travelling along the x-axis is described by the equation y(x, t) = (4 cm) sin[(0.5 cm) x - (1.05 s<sup>-1</sup>) t) ]. What is the wavelength of the wave? A) 0.5 cm B) 1.05 cm C) 4.0 cm D) 12.6 cm

The figure shows a wave in a rope with two points labelled A and B.
-A harmonic wave travelling along the x-axis is described by the equation y(x, t) = (4 cm) sin[(0.5 cm) x - (1.05 s^-1) t) ]. What is the wavelength of the wave?

Quizplus · Accepted Answer

The wavelength ($\lambda$) of a wave is related to its wave number (k) by the equation $\lambda = \frac{2\pi}{k}$. In the given wave equation $y(x, t) = (4 cm)\sin[(0.5 cm^{-1})x - (1.05 s^{-1})t]$, the wave number $k = 0.5 cm^{-1}$. Therefore, the wavelength $\lambda = \frac{2\pi}{0.5 cm^{-1}} = 4\pi cm \approx 12.6 cm$.

Figure 142 the Figure Shows a Wave in a Rope