Using special techniques called$$string harmonics$($or "flageolet tones"$),$ stringed instruments can produce the first few overtones of the harmonic series. While a violinist is playing some of these harmonics for us$,$ we take a picture of the vibrating string $($see figures$).$ Using an oscilloscope, we find the violinist plays a note with frequency$$f$=790$Hz in figure $($a$).$ Part $($a$)$ How many nodes does the standing wave in figure $($a$)$ have?Part $($b$)$How many antinodes does the standing wave in figure $($a$)$ have?$$Part $($c$)$The string length of a violin is about$$L $=33$ cm$.$ What is the wavelength of the standing wave in figure $($a$)$ in meters?$$Part $($d$)$The fundamental frequency is the lowest frequency that a string can vibrate at $($see figure $($b$)).$ What is the fundamental frequency for our violin in hertz?$$Part $($e$)$In terms of the fundamental frequency$$f$1,$ what is the frequency of the note the violinist is playing in figure $($c$)?$Part $($f$)$Write a general expression for the frequency of any note the violinist can play in this manner, in terms of the fundamental frequency,$$f$1,$ and n$,$ the number of antinodes on a standing wave. Part $($g$)$What is the frequency, in hertz, of the note the violinist is playing in figure $($d$)?$