You are testing a sonar machine underwater by sen ding out sound waves to measure distances. Using the graphical representations shown for the wave, find the amplitude, frequency, wavelength, and speed of the wave, and write a mathematical representation of the wave.

**Requirement** In this exercise, we have two labelled graphical representation of a wave. We have to use the information they provide to us to write the wave's mathematical representation. **Key concept** Mathematic representation of a wave has two dependence equation that describe it: 1. Dependence on position, which follows the formula: $$\begin{align} \mathrm{y(x)}=\mathrm{A \cdot \sin \left(\frac{2\pi \cdot x}{\lambda}\right)} \end{align}$$ 2. Dependence on time, which follows the formula: $$\begin{align} \mathrm{y(x)}=\mathrm{A \cdot \sin \left(2\pi \cdot f \cdot t\right)} \end{align}$$ All we have to do is find the values of parameters and simply insert them into their respective equations. There is also one more parameter we need, and that is **period**, which is: $$\begin{align} \mathrm{T=\frac{1}{f}} \end{align}$$ which represents the point at which **the cycle repeats**. This will be relevant later.

You are testing a sonar machine underwater by sen ding out s

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Requirement

In this exercise, we have two labelled graphical representation of a wave. We have to use the information they provide to us to write the wave's mathematical representation.

Key concept

Mathematic representation of a wave has two dependence equation that describe it:

Dependence on position, which follows the formula:

\begin{align} \mathrm{y(x)}=\mathrm{A \cdot \sin \left(\frac{2\pi \cdot x}{\lambda}\right)} \end{align}

Dependence on time, which follows the formula:

\begin{align} \mathrm{y(x)}=\mathrm{A \cdot \sin \left(2\pi \cdot f \cdot t\right)} \end{align}

All we have to do is find the values of parameters and simply insert them into their respective equations.

There is also one more parameter we need, and that is period, which is:

\begin{align} \mathrm{T=\frac{1}{f}} \end{align}

which represents the point at which the cycle repeats. This will be relevant later.

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Rope	Density $(\mathrm{kg} / \mathrm{m})$	Wavelength $(\mathrm{m})$	Frequency $(\mathrm{Hz})$	Speed $(\mathrm{m} / \mathrm{s})$
1	$0.25$	$3.16$	$2.00$	$6.32$
1	$0.25$	$1.58$	$4.00$	$6.32$
2	$0.15$	$4.08$	$2.00$	$8.16$
2	$0.15$	$2.04$	$4.00$	$8.16$

Rope	Density $(\mathrm{kg} / \mathrm{m})$	Wavelength $(\mathrm{m})$	Frequency $(\mathrm{Hz})$	Speed $(\mathrm{m} / \mathrm{s})$
1	$0.25$	$3.16$	$2.00$	$6.32$
1	$0.25$	$1.58$	$4.00$	$6.32$
2	$0.15$	$4.08$	$2.00$	$8.16$
2	$0.15$	$2.04$	$4.00$	$8.16$

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You are testing a sonar machine underwater by sen ding out sound waves to measure distances. Using the graphical representations shown for the wave, find the amplitude, frequency, wavelength, and speed of the wave, and write a mathematical representation of the wave.

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