AP Physics 2 Exam Question:

Consider a wave traveling in the x-direction given by the function:

where x is in meters and t is in seconds. Answer the following questions based on this wave:

(a) Determine the wavelength and frequency of the wave.

(b) Calculate the amplitude of the wave.

(c) Find the speed of the wave.

Solution:

(a) To find the wavelength of the wave, we can identify the coefficient of x in the equation. The coefficient of x in the equation is $\dfrac{4\pi}{2\pi} = 2$. The wavelength, $\lambda$, is given by the formula $\lambda = \dfrac{2\pi}{k}$, where k is the coefficient of x. Therefore:

The frequency of the wave, $f$, can be determined from the coefficient of t in the equation. The coefficient of t is $\dfrac{-10\pi}{2\pi} = -5$. The frequency is given by the formula $f = \dfrac{-k}{2\pi}$, where k is the coefficient of t. Therefore:

(c) The speed of the wave, v, can be determined using the formula $v = \lambda f$. Substituting the known values:

Therefore, the answers to the questions are:

(a) The wavelength of the wave is $\pi$ meters and the frequency is $\dfrac{5}{2\pi}$ Hz.

(b) The amplitude of the wave is 0.05 meters.

(c) The speed of the wave is $\dfrac{5}{2}$ m/s.