3. To study the behavior of the waves, take a cable 4Kg mass and 20 m long, this

Question

3. To study the behavior of the waves, take a cable 4Kg mass and 20 m long, this is attached to an oscillator, and the other end is passed by a fixed pulley that is 16 m from the oscillator. At the free end, 40 kg are hung and the oscillator starts to work. It is observed that 15 waves are formed with an amplitude of 30 cm. Determine: a) the speed of the waves, b) the length of the waves formed, c) the frequency, d) the energy per unit length, e) the power. For that system, f) what will be the fundamental frequency and the seventh over-tone? 3. To study the behavior of the waves, take a cable 4Kg mass and 20 m long, this is attached to an oscillator, and the other end is passed by a fixed pulley that is 16 m from the oscillator. At the free end, 40 kg are hung and the oscillator starts to work. It is observed that 15 waves are formed with an amplitude of 30 cm. Determine: a) the speed of the waves, b) the length of the waves formed, c) the frequency, d) the energy per unit length, e) the power. For that system, f) what will be the fundamental frequency and the seventh over-tone?

Explanation / Answer

linear mass density of cable, mue = 4/20 = 0.2 kg/m

tension in the cable, T = M*g

= 40*9.8

= 392 N

a) speed of the wave, v = sqrt(T/mue)

= sqrt(392/0.2)

= 44.3 m/s

b) wavelength, lamda = 16/15

= 1.07 m

c) f = v/lamda

= 44.3/1.07

= 41.4 Hz

d) Energy per unit length = 2*pi^2*f^2*A^2*mue

= 2*pi^2*41.4^2*0.3^2*0.2

= 609 J/m

e) Power = Enegy per unit length*v

= 609*44.3

= 2.7*10^4 W

f) fo = v/(2*L)

= 44.3/(2*16)

= 1.38 Hz

7th overtone = 8th harmonic

= 8*1.38

= 11.0 Hz

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