AP Physics 1 Exam Question

A wave is traveling along a string with a frequency of 10 Hz and a wavelength of 2 meters. The wave is moving in the positive x-direction.

a) Calculate the wave speed.

b) Determine the period of the wave.

c) If the wave has an amplitude of 0.5 meters, what is the maximum displacement of the particles in the medium?

d) Explain how the wave transfers energy.

e) If the frequency of the wave doubles while the wavelength remains constant, what will happen to the wave speed?

Answer:

a) The wave speed can be calculated using the formula:

Wave speed = Frequency x Wavelength

Substituting the given values:

Wave speed = 10 Hz x 2 m
           = 20 m/s

Therefore, the wave speed is 20 m/s.

b) The period can be found by using the formula:

Period = 1 / Frequency

Substituting the given frequency:

Period = 1 / 10 Hz
       = 0.1 s

Therefore, the period of the wave is 0.1 seconds.

c) The maximum displacement of the particles can be found using the amplitude:

Maximum displacement = Amplitude
                    = 0.5 meters

Therefore, the maximum displacement of the particles is 0.5 meters.

d) The wave transfers energy through the oscillation of particles in the medium. As the wave propagates, the particles in the medium oscillate back and forth around their equilibrium positions. This oscillation creates a transfer of energy from one particle to the next, propagating the wave along the medium.

e) If the frequency of the wave doubles while the wavelength remains constant, the wave speed will also double. This is because the wave speed is determined by the product of frequency and wavelength. As the frequency increases, the wave speed will also increase proportionally, as long as the wavelength remains constant.