Calculating Water Wave Frequency

Investigation of Water Wave Frequency

In part (c) of this physics investigation, the student examines the properties of a specific water wave to determine its frequency based on provided physical parameters. The experimental data identifies the wavelength of the water wave as $0.05\,m$ and the wave speed as $0.075\,m/s$. This problem serves as a practical application of the wave equation within the study of wave mechanics.

The Wave Equation and Mathematical Relationship

The fundamental relationship between wave speed, frequency, and wavelength is governed by the wave equation. This principle states that the speed at which a wave travels through a medium is the product of its frequency and its wavelength. The formula is expressed as $v = f \times \lambda$. In this scenario, the student is tasked with calculating the frequency ($f$). To do so, the formula must be algebraically rearranged to isolate frequency, resulting in the expression $f = \frac{v}{\lambda}$. This mathematical structure indicates that frequency is inversely proportional to wavelength when the wave speed remains constant.

Step-by-Step Calculation and Working

The student provides explicit working to reach the final answer, which is a requirement for the $3$ marks allocated to this sub-question. First, the known values are substituted into the rearranged wave equation. The wave speed ($v$) of $0.075\,m/s$ is placed in the numerator, and the wavelength ($\lambda$) of $0.05\,m$ is placed in the denominator. The calculation is set up as follows: $f = \frac{0.075}{0.05}$. By executing this division, the numerical value for the frequency is determined to be $1.5$.

Results and Exam Distribution

The final calculated frequency of the water wave is $1.5\,\text{Hz}$. The unit Hertz ($\text{Hz}$) represents cycles per second, signifying that $1.5$ full wave cycles pass a fixed point every second. This specific component of the study comprises $3$ marks of the total marks awarded for the section. The transcript indicates that the total for Question 10 is $5$ marks, highlighting the relative importance of the calculation and the showing of work in the overall assessment of the student's investigation.