**Chapter 11 Lesson 1b: Properties of Waves**
"I can explain the properties of waves."
April 7, 2020
Caleb Bibb
>>>
>>> Press f to use presentation mode
>>> Press n to open a window with the notes.
>>>
---
## Remember our surfer.
>>>
>>> * Remember we talked about our surfer.
>>> * What makes some waves great surfing waves like this one, and others terrible waves?
>>> * Why are some waves nice and big and smooth, while others are small and choppy?
>>>
---
## Transverse Waves
>>>
>>> * Remember that transverse waves have high points called crests and low points called troughs
>>> * Longitudinal waves do not have crests and troughs.
>>>
---
>>>
>>> * Longitudinal waves have compression points and Rarefaction points
>>> * compression points are when more particles are bumping into each other
>>> * particles in a Longitudinal wave move parallel with the wave (they move in the direction of the wave)
>>>
---
## Wavelength
$$\lambda = \text{Wavelength}$$
>>>
>>> Amplitude is the distance from the center line of the wave to the top or bottom of the wave.
>>>
---
## Frequency
$$ 1 \text{ Hz} = \frac{1}{\text{s}}$$
| Type | Hertz |
|:----------------:|:--------------------------:|
| Earthquake waves | 0.5 |
| Microwaves | 100,000,000,000 |
| Radio waves | 100,000,000 |
| Sound (middle C) | 512 |
| X-rays | 10,000,000,000,000,000,000 |
>>>
>>> * The number of waves that pass through a specific point in a given time is the frequency.
>>> * We measure frequency in Hertz which is the number of something per second.
>>>
---
## We Try 1:
If two wavelengths pass a certain point in one second, what is the frequency?
>>>
>>> $$ \frac{2 \lambda}{1 \text{s}} = 2 \text{ Hz}$$
>>>
---
## Speed
$$
\begin{align}
\text{speed } (v) &= \text{wavelength } (\lambda) \times \text{frequency } (f)\\
\\
v &= \lambda \times f
\end{align}
$$
So, for a wave with wavelength of 5 m and a frequency of 4 Hz.
Then its speed is
$$
v = 5 \text{ m} \times 4 \text{ Hz} = 20 \frac{\text{m}}{\text{s}}
$$
>>>
>>> * Now is when everything comes together.
>>>
---
## You Try 1:
If two waves have the same
wavelength and the same frequency, what
can you infer about the speed of the two
waves?
>>>
>>> Since speed is wavelength times frequency, then they would have the same speed.
>>>
---
## At a constant speed (like with light for example)
$$v = \lambda \times f$$
$$
\begin{align}
\frac{v}{f} &= \frac{\lambda \times f}{f}\hfill \hfill &\frac{v}{\lambda}&=\frac{\lambda \times f}{\lambda}\\
\\
\frac{v}{f} &= \lambda \hfill \hfill &\frac{v}{\lambda}&=f\\
\end{align}
$$
>>>
>>> * We can see from our equations that frequency and wavelength are inversely proportional.
>>> * inversely proportional means that when one increases, the other decreases when we have a constant speed.
>>>
---
## We Try 2:
You conduct an experiment
with a spring toy and find that
the wavelength is 0.6 m and the
frequency is 3.5 Hz. What is the
speed of the wave?
---
## We Answer 2:
$$
\lambda = 0.6 \text{m},\\
f = 3.5 \text{ Hz} = \frac{3.5}{\text{s}}\\
\\
\\
\begin{align}
v &= \lambda \times f \\
v &= \left( 0.6 \text{ m} \right) \left( \frac{3.5}{\text{s}} \right)\\
v &= 2.1 \frac{\text{m}}{\text{s}}
\end{align}
$$
---
## You Try 2:
In a second trial, you calculate the speed of
the wave to be 2.16 m/s and the
frequency to be 1.2 Hz. What is the
wavelength?
---
## You Answer 2:
$$
v = \frac{2.16 \text{ m}}{\text{s}},\\
f = 1.2 \text{ Hz} = \frac{1.2}{\text{s}}\\
\\
\\
\begin{align}
\frac{v}{f} &= \lambda\\
\frac{\frac{2.16\text{ m}}{\text{s}}}{\frac{1.2}{\text{s}}} &= \lambda \\
1.8 \text{ m} &= \lambda
\end{align}
$$