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Wave speed is a fundamental concept in the study of transverse waves. It is the rate at which waves travel through a medium, such as a string or air. This concept is essential for understanding how fast wave information is transmitted. The wave speed (\(v\)) can be determined from two other key properties of the wave: frequency (\(f\)) and wavelength (\(\lambda\)). The relationship is described by the equation:\[v = f \lambda\]This formula tells us that the speed of the wave is the product of its frequency and wavelength. For the wave in our original exercise, with a wave speed of 8.00 m/s and a wavelength of 0.320 m, it allows us to calculate the frequency easily.

Frequency is one of the vital characteristics of a wave. It tells us how many wave cycles pass a given point per second. Measured in hertz (Hz), frequency is fundamental in determining how often the wave pattern repeats itself. In our exercise, given the wave speed of 8.00 m/s and a wavelength of 0.320 m, we can use the formula:\[f = \frac{v}{\lambda} = \frac{8.00 \, \text{m/s}}{0.320 \, \text{m}} \approx 25.00 \, \text{Hz}\]From this, we find the frequency to be 25 Hz. Knowing this allows us to understand how quickly the wave pattern repeats, which is helpful when predicting behaviors of the wave over time.

The wave function is a mathematical representation that describes the shape and position of a wave at any given time. For transverse waves traveling in the -x direction, the wave function has the general form:\[\psi(x,t) = A\sin(kx - \omega t)\]Here, \(A\) is the amplitude, \(k\) is the wave number, and \(\omega\) is the angular frequency. In our specific example, the amplitude is 0.0700 m, the wave number is calculated as:\[k = \frac{2\pi}{\lambda} = \frac{2\pi}{0.320 \, \text{m}} \approx 19.63 \, \text{rad/m}\]The angular frequency \(\omega\) is:\[\omega = 2\pi f = 2\pi \times 25 \, \text{Hz} \approx 157.08 \, \text{rad/s}\]Thus, the wave function can be finalized as:\[\psi(x,t) = 0.0700 \sin(19.63 \, \text{rad/m} \cdot x - 157.08 \, \text{rad/s} \cdot t)\]

Maximum displacement refers to the furthest point that a particle in the wave reaches from its equilibrium position. This is also known as the amplitude of the wave. In the exercise, the transverse wave has a maximum displacement (amplitude) of 0.0700 m. To calculate the transverse displacement of a particle at any point, we use the wave function:\[\psi(x,t) = A\sin(kx - \omega t)\]If we want to know the displacement at a specific moment and position, for example, at \(x=0.360 \, \text{m}\) at \(t=0.150 \, \text{s}\), it involves substituting these values into the wave function to get:\[\psi(0.360 \, \text{m}, 0.150 \, \text{s}) = 0.0700 \sin(19.63 \, \text{rad/m} \cdot 0.360 \, \text{m} - 157.08 \, \text{rad/s} \cdot 0.150 \, \text{s})\]Calculating this will yield the specific displacement of that wave section at the given time.