7. Wave Speed A steel wire of length 30.0 m and a copper wire of length 20.0 m,

Question

7. Wave Speed A steel wire of length 30.0 m and a copper wire of length 20.0 m, both with 1.00-mm diameters, are connected end to end and stretched to a tension of 150 N. During what time interval will a transverse wave travel the entire length of the two wires? 8. Wave Speed The lower end of a uniform bar of mass 45.0 kg is attached to a wall by a frictionless hinge. The bar is held by a horizontal wire attached at its upper end so that the bar makes an angle of 30.0° with the wall. The wire has length 0.330 m and mass 0.0920 kg. (a) What is the frequency of the fundamental standing wave for transverse waves on the wire? (b) Is this an audible frequency for humans? 9. A vibrating string 50.0 cm long is under a tension of 1.00 N. The results from five successive stroboscopic pictures are shown. The strobe rate is set at 5000 flashes per minute, and observations reveal that the maximum displacement occurred at flashes 1 and 5 with no other maxima in between. (a) Find the period, frequency, and wavelength for the traveling waves on this string. (b) In what normal mode(harmonic) is the string vibrating? (c) What is the speed of the traveling waves on the string? (d) How fast is point P moving when the string is in () position 1 and ii) position 3? (e) What is the mass of this string? 1.5 cm 1.5 cm

Explanation / Answer

7. density of steel = 8050 kg /m^3

linear mass density, mu = density * cross section area

cross section area = pi (1 x 10^-3/ 2)^2

=7.854 x 10^- 7 m^2

mu1 = 6.322 x 10^-3 kg/m

v1 = sqrt[ T / mu1 ]= sqrt[ 150 / (6.322 x 10^-3) ]

v1 = 154 m/s

for copper wire, density = 8960 kg/m^3

mu2 = 7.037 x 10^-3 kg/m

v2 = 146 m/s

t= (30/154) + (20 / 146)

= 0.332 sec  

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