Question:
A wave traveling through a medium has a wavelength of 2 meters and a frequency of 10 Hz. The wave also has an amplitude of 0.5 meters. Determine the speed, period, and maximum particle velocity of the wave.
Answer:
Given: Wavelength, λ = 2 m Frequency, f = 10 Hz Amplitude, A = 0.5 m
The speed of a wave is calculated using the formula:
v = λ × f
Plugging in the given values:
v = 2 m × 10 Hz
v = 20 m/s
Therefore, the speed of the wave is 20 m/s.
The period of a wave is the time taken for one complete wave cycle. It is calculated using the formula:
T = 1/f
Plugging in the given values:
T = 1/10 Hz
T = 0.1 s
Therefore, the period of the wave is 0.1 s.
The maximum particle velocity (v_max) of a wave is calculated using the formula:
v_max = 2π × f × A
Plugging in the given values:
v_max = 2π × 10 Hz × 0.5 m
v_max = 10π m/s
Therefore, the maximum particle velocity of the wave is 10π m/s.
In summary, we have determined that the speed of the wave is 20 m/s, the period of the wave is 0.1 s, and the maximum particle velocity of the wave is 10π m/s.