Hi! I really need help with part C as I am not sure how the mass per unit length

Question

Hi! I really need help with part C as I am not sure how the mass per unit length ties in... You have tuning forks (which oscillate at a fixed frequency stamped on the fork) for frequenciesof 294 Hz and 300 Hz. (A) What beat frequency is heard when you play both forks at the sametime?(6hz) (B) If you have an (untuned) string which makes for a beat frequency of 8 Hz against the 294Hz fork and 2 Hz against the 300 Hz fork, what frequency is the string emitting?(302hz) (C) If the string is 91.44 cm long, has a mass per unit length of 0.4 g/m, and is vibrating in its fundamental mode, what change in string tension is needed to bring the string into tune with the 294 Hz fork? (Either anabsolute change in newtons, or a multiplicative factor to the tension, makes an acceptable answer.)

Explanation / Answer

C) In fundamental mode,

wavelength = 2L

frequency = speed of wave / wavelength

294 Hz = v / (2 x 0.9144 m)

v = 537.67 m/s

and speed v = sqrt(T / mass per unit length)

mass per unit length= 0.4 x 10^-3 kg / m

537.67 = sqrt(T / (0.4 x 10^-3))

T = 115.63 N

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