The second resonant frequency (a.k.a second harmonic, n=2) of a string of length

Question

The second resonant frequency (a.k.a second harmonic, n=2) of a string of length 60cm has the same frequency as the third resonant frequency (a.k.a. fifth harmonic, n=5) of a 1.0m pipe that is open only at one end. The linear mass density of the string is, u=0.0012 kg/m. Take the speed of sound to be vsound=341m/s. a) Find the tension in the string. b)Find the velocity of the wave on the string when the tension of part (a) is doubled. c) Find the new second frequency (a.k.a. second harmonic) once the tension is doubled. Please explain.

Explanation / Answer

n= 5 so, 5/4 = 1

= 4/5 = 0.8 m

v= 341

f= 426.25 Hz

this is equal to n= 2 of string so,

3/2 = 60 cm

= 40 cm = 0.4 m

a. velocity = f X =  170.5

b. when tension is doubled , frequency is

v1/v2 = sqrt( t2/t1 )

velocityv2= = 241.123 m/s

c. new harmonic frequency = v2/ = 602.8 Hz

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