AP Physics 2 Exam Question:

Consider a wave traveling through a medium. The wave has a wavelength of 2.5 m and a frequency of 60 Hz. The wave travels at a speed of 150 m/s.

a) Calculate the period of the wave. b) Determine the amplitude of the wave. c) Find the wave number of the wave. d) Calculate the angular frequency of the wave.

Answer:

a) Period of a wave (T) is the time it takes for one complete cycle. It is defined as the reciprocal of the frequency (f).

Given: Wavelength (λ) = 2.5 m Frequency (f) = 60 Hz

To find the period (T), we use the equation: T = 1 / f

Substituting the given values: T = 1 / 60 Hz = 0.0167 s

Therefore, the period of the wave is 0.0167 seconds.

b) Amplitude of a wave (A) is the maximum displacement of particles in the medium from their equilibrium positions.

Given that the wave has an amplitude of 0.2 m.

Therefore, the amplitude of the wave is 0.2 meters.

c) Wave number (k) is the reciprocal of the wavelength (λ). It represents the spatial frequency of the wave.

Given: Wavelength (λ) = 2.5 m

To find the wave number (k), we use the equation: k = 1 / λ

Substituting the given value: k = 1 / 2.5 m = 0.4 rad/m

Therefore, the wave number of the wave is 0.4 rad/m.

d) Angular frequency (ω) is the number of radians a wave travels in one second. It can be calculated using the equation:

ω = 2πf

Given: Frequency (f) = 60 Hz

Substitute the given value: ω = 2π(60 Hz) = 377 rad/s

Therefore, the angular frequency of the wave is 377 radians per second.

In summary, a) The period of the wave is 0.0167 seconds. b) The amplitude of the wave is 0.2 meters. c) The wave number of the wave is 0.4 rad/m. d) The angular frequency of the wave is 377 radians/second.