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Standing Waves

Standing waves on a string have a number of relevant variables:

• The length $L$ of the standing wave is the distance between the ends.
• The speed $v$ is the speed a wave would have if it travelled along the string.
• The mode $n$ of the standing wave is the number of antinodes: that is, the number of crests or troughs.
• The frequency $f_n$ of the nth mode is the frequency of the antinodes as they move up and down.
• The wavelength ${\lambda }_n$ is the distance between two crests, two troughs, etc. It is related to the length as $${\lambda }_n=\frac{2L}{n}$$
• The fundamental frequency $f_1$ is the lowest frequency that can exist on this string. It is given by $$f_1=\frac{v}{2L}$$, and it is related to the frequency of the $n$th mode by $$f_n=n{f}_1$$

I suggest you start by listing these six variables, fill in what is given, and then find the appropriate equations to find the variable you want.