A vibrating string 45.0 cm long is under a tension of 1.03 N . The results from

Question

A vibrating string 45.0 cm long is under a tension of 1.03 N . The results from five successive stroboscopic pictures are shown in the figure. The strobe rate is set at 5000 flashes per minute, and observations reveal that the maximum displacement occured at flashes 1 and 5 with no other maxima in between.

a) Find the period for the traveling waves on this string.

T = _______________ s

b) Find the frequency for the traveling waves on this string.

f = _________________ Hz

c) Find the wavelength for the traveling waves on this string.

d) In what harmonic is the string vibrating?

n = ______________________

e) What is the speed of the traveling waves on the string?

v = __________________ m/s

f) How fast is point P moing when the string is in position 1?

v = ____________________ m/s

Explanation / Answer

a) thw string vibrate through 1/2 cycle in 4 * 1/5000 min

1/2 T = 4 / 5000

T = 1.6 * 10-3 min = 9.6 * 10-2 s

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b) f = 5000 flashes / 1 min * 1 cycle / 8 flashes * 1min / 60s

= 10.42 Hz

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c) lambda = L

= 45.0 cm

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d) second harmonic

n = 2

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e) v = lambda * f

= 0.45 * 10.4

= 4.68 m/s

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f) speed vy = w (1.5 cm) sin kx sin wt

sin kx = sin wt = 1

vy = w (1.5 cm) = 2pi f (1.5 cm)

= 2pi * 10.4 (1.5 cm)

vy = 0.98 m/s

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