find the fundamental frequency at which standing wave could vibrate on the follo

Question

find the fundamental frequency at which standing wave could vibrate on the following string. The string is 30cm long with a linear mass density of .65g/m.It is subjected to 45 Newtons of tenssion. two strings vibrate in phase with each other both at the frequency found in the first part of the question. Sounf travels through the air from these strings at approximately 340m/s. The two strings are separated by a meter. In in centimeters find the position closest to the midpoint between these two strings at which a receiver or ear could be placed and hear nothing at all

Explanation / Answer

given that l = 30 cm = 0.3 m

linear mass density mu = 0.65*10^-3 kg/m

T = 45 N

fundamental frequency is f = (1/2l)*sqrt(T/mu)

f = (1/(2*0.3))*sqrt(45/(0.65*10^-3))

f = 438.52 Hz

wavelength of waves received by the ear is lamda = v/f = 340/438.52 = 0.775 m

path differnce is d-(1-d) = lamda/2

2d-1 = 0.775/2 = 0.3875 m

2d = 1+0.3875= 1.3875

d = 1.3875/2

d = 0.7 m

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