When the Low E string of a correctly$-$tuned acoustic guitar vibrates openly $($without being pressed

against the fretboard$),$ the frequency of the fundamental mode of vibration is $82\mathrm{.}0$ Hz$.$ The Low

E string is $64\mathrm{.}0$ cm long, and the wavelength of the fundamental mode is twice the length of the

string. If the Low E string has a mass of $6\mathrm{.}50$ grams, calculate:

a$)$ The linear mass density of the string.

b$)$ The speed of the wave on the string.

c$)$ The tension in the string.

d$)$ If this guitar string vibrated in a room with a temperature of $30$ C$,$ find the speed of sound

of this vibration in the air in the room.