AP Physics 2 Exam Question

A wave is traveling in a medium with a wavelength of 2.0 meters and a frequency of 50 Hz. The amplitude of the wave is 0.5 meters. The wave is incident on a boundary where the medium changes, causing the wave to be partially reflected and partially transmitted. The reflected wave has an amplitude of 0.3 meters.

a) Calculate the speed of the wave in the medium.

b) Determine the period and angular frequency of the wave.

c) Using the Law of Reflection, calculate the angle of incidence when the wave is incident normal to the boundary.

d) Calculate the intensity of the transmitted wave if the intensity of the incident wave is 150 W/m².

Answer

a) The speed (v) of a wave can be calculated using the formula: v = λ * f, where λ is the wavelength and f is the frequency.

Given:

Wavelength (λ) = 2.0 meters Frequency (f) = 50 Hz

Substituting the values into the formula: v = 2.0 m * 50 Hz = 100 m/s

Therefore, the speed of the wave in the medium is 100 m/s.

b) The period (T) of a wave is the reciprocal of its frequency (T = 1/f), and the angular frequency (ω) is given by ω = 2πf.

Given:

Frequency (f) = 50 Hz

Calculating the period: T = 1/50 Hz = 0.02 s

Calculating the angular frequency: ω = 2πf = 2π * 50 Hz = 100π rad/s

Therefore, the period of the wave is 0.02 s and the angular frequency is 100π rad/s.

c) According to the Law of Reflection, the angle of incidence (θ) is equal to the angle of reflection.

Given: wave is incident normal to the boundary

When a wave is incident normal to a boundary, the angle of incidence equals 0 degrees.

Therefore, the angle of incidence when the wave is incident normal to the boundary is 0 degrees.

d) The intensity (I) of a wave is given by the formula: I = (A^2) * (ω * ρ * v), where A is the amplitude, ω is the angular frequency, ρ is the density of the medium, and v is the speed of the wave.

Given:

Amplitude (A) = 0.5 meters Angular frequency (ω) = 100π rad/s Speed (v) = 100 m/s Intensity of incident wave (I_incident) = 150 W/m²

Substituting the values into the formula: I_transmitted = (0.5^2) * (100π * ρ * 100)

To calculate the intensity of the transmitted wave, we need to know the value of ρ, the density of the medium. Since this value is not provided in the question, further calculations cannot be performed.

Therefore, we cannot calculate the intensity of the transmitted wave without knowing the density of the medium.