# Physics Study Guide/Standing waves


------------------------------------------------------------------------

# Standing waves

  ----------------------------------------------
   $\|\vec{v}\|=\sqrt{\frac{\|\vec{T}\|}{\mu}}$
  ----------------------------------------------

**Wave speed** is equal to the square root of **tension** divided by the
**linear density** of the string.

+-------------------------------------------------+
| ```{=html}                                      |
| <div style="text-align: center;">               |
| ```                                             |
| `<big>`{=html}***μ* = *m*/*L*** `</big>`{=html} |
|                                                 |
| ```{=html}                                      |
| </div>                                          |
| ```                                             |
+-------------------------------------------------+

**Linear density** of the string is equal to the **mass** divided by the
**length** of the string.

+---------------------------------------------------+
| ```{=html}                                        |
| <div style="text-align: center;">                 |
| ```                                               |
| `<big>`{=html}***λ*~max~ = 2*L*** `</big>`{=html} |
|                                                   |
| ```{=html}                                        |
| </div>                                            |
| ```                                               |
+---------------------------------------------------+

The **fundamental wavelength** is equal to two times the **length** of
the string.

```{=html}
<H2>
```
Variables

```{=html}
</H2>
```
\

+---------------------------------------+
| *λ:* wavelength (m)\                  |
| *λ~max~:* fundamental wavelength (m)\ |
| *μ:* linear density (g/m)\            |
| *v:* wave speed (m/s)\                |
| *F:* force (N)\                       |
| *m:* mass (kg)\                       |
| *L:* length of the string (m)\        |
| *l:* meters (m)                       |
+---------------------------------------+

```{=html}
<H2>
```
Definition of terms

```{=html}
</H2>
```
+----------------------------------------------------------------------+
| **Tension (*F*):** (not frequency) in the string (*t* is used for    |
| time in these equations). Units: newtons (N)\                        |
| \                                                                    |
| **Linear density (*μ*):** of the string, Greek mu. Units: grams per  |
| meter (g/m)\                                                         |
| \                                                                    |
| **Velocity (*v*)** of the wave (m/s)\                                |
| \                                                                    |
| **Mass (*m*)**: Units: grams (g). (We would use kilograms but they   |
| are too big for most strings).\                                      |
| \                                                                    |
| **Length of the string (*L*):** Units: meters (m)                    |
+----------------------------------------------------------------------+

Fundamental frequency: the frequency when the wavelength is the longest
allowed, this gives us the lowest sound that we can get from the system.

In a string, the length of the string is half of the largest wavelength
that can create a standing wave, called its fundamental wavelength.
