A (infinitely long) string oscillates according to the equation: y(x,t) = (0.40
ID: 2173109 • Letter: A
Question
A (infinitely long) string oscillates according to the equation:y(x,t) = (0.40 cm) sin[ (pi/3 cm^-1) x ] cos[ (50pi s^-1) t ]
(a) Find the following quantities for each of the two travelling waves (identical except for direction of travel) which create this oscillation:
Amplitude =.2cm/s
Wave speed 150cm/s
Period =____s
(b) For the standing wave observed, what is the distance:
between adjacent nodes?____cm
between adjacent anti-nodes?____cm
(c) For a point of the medium located at x = 1 cm,
What is the period of its oscillation?____s
What is the maximum speed of this point?____cm/s
and at what distance (+) from y=0 along the y-axis does it occur?____cm
What is the maximum acceleration of this point____cm/s2
and at what distance (+) from y=0 along the y-axis does this occur?____cm
What is the size of the maximum concavity of the string at this location during the oscillation?____cm-1
(Hint: There is a nice shortcut here.)
Explanation / Answer
a)Amplitude =.20cm/s Wave speed =150cm/s Period = .04 s (b) For the standing wave observed, what is the distance: between adjacent nodes? 3 cm between adjacent anti-nodes? 3 cm (c) For a point of the medium located at x = 1 cm, What is the maximum speed of this point?=54.4 cm/s and at what distance (+) from y=0 along the y-axis does it occur?=.35 cm What is the maximum acceleration of this point =8545.13cm/s2 and at what distance (+) from y=0 along the y-axis does this occur?=.35cm What is the size of the maximum concavity of the string at this location during the oscillation ???????
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