Estimate the average power of a moving water wave that strikes the chest of an adult standing in the water at the seashore. Assume that the amplitude of the wave is 0.50 m, the wavelength is 2.5 m, and the period is 4.0 s.

Verified step by step guidance

1. Calculate the angular frequency ($\omega$) of the wave using the formula $\omega =\frac{2\pi }{T}$, where $T$ is the period of the wave.
2. Determine the wave number ($k$) using the formula $k=\frac{2\pi }{\lambda }$, where $\lambda$ is the wavelength of the wave.
3. Use the formula for the speed of the wave ($v$), which is $v=\lambda \times f$, where $f$ is the frequency of the wave. Frequency can be calculated as $f=\frac{1}{T}$.
4. Calculate the energy density ($u$) of the wave using the formula $u=\frac{1}{2}\rho g{A}^2$, where $\rho$ is the density of water, $g$ is the acceleration due to gravity, and $A$ is the amplitude of the wave.
5. Estimate the average power ($P$) using the formula $P=u\times v$, where $u$ is the energy density calculated in the previous step and $v$ is the speed of the wave.

Key Concepts

Wave Properties

Understanding wave properties such as amplitude, wavelength, and period is essential for analyzing wave behavior. Amplitude refers to the maximum displacement of points on a wave, wavelength is the distance between successive crests, and period is the time taken for one complete cycle of the wave. These properties influence the energy and power carried by the wave.

Power of Waves

The power of a wave is defined as the rate at which energy is transferred by the wave. It can be calculated using the formula P = E/T, where P is power, E is energy, and T is time. In the context of water waves, the energy is related to the wave's amplitude and frequency, which affects how much force is exerted on objects in the water.

Energy Transfer in Water Waves

Water waves transfer energy through the motion of water particles, which oscillate in circular or elliptical paths. The energy carried by the wave can be estimated using the wave's amplitude and frequency, as larger amplitudes and higher frequencies result in greater energy transfer. This energy is what impacts objects, such as a person standing in the water, when waves strike them.