A 0.1 Kg mass vibrates according to the equation X (t) = 1 42cos7.40t, where x I
ID: 1538936 • Letter: A
Question
A 0.1 Kg mass vibrates according to the equation X (t) = 1 42cos7.40t, where x Is In meters and t is in seconds. Determine: The velocity and acceleration as a function of time The amplitude The frequency The total energy An observer is standing on the platform of a railway station. A train Roes through the station without stopping. If the frequency of the train whistle decreases by a factor of 1/2 as it approaches and then passes him, calculate the speed of the train (assume the speed of sound in air = 343 m/s). In a set of open - open rank of pipes, the length of the longest pipe is 5.0 m. Take the speed of sound to be 340 m/s. Draw diagrams showing the fundamental, first and second overtone displacement nodes and antinodes. Determine the fundamental frequency of the longest pipe. What would be the fundamental frequency of a closed pipe (closed at one end) of the same length? When a pin of mass 0.200 grams is dropped from a height of 1.00 m, 10% of its energy converted into a sound pulse that has a duration of 0.100s. Find how far away the dropped pin can be heard if the audible intensity at that point is 1.00 times 10^-8W/m^2, the intensity is given by the equation l=P/4 pi r^2). What is the intensity level at that point? An ambulance siren has a fundamental frequency of 261. Hz. The ambulance travels at 26 m/s. In front of the ambulance is a police car traveling at 30.0 m/s. Take the speed of sound as 342.5 m/s. What is the frequency of the ambulance as heard by the police car? What is the frequency heard back at the ambulance after it reflected off the police car?Explanation / Answer
here,
mass , m = 0.1 kg
X(t) = 1.42 * cos(7.4 * t) ......(1)
a)
differentiating equation (1) for v
v(t) = - 10.51 *sin(7.4 * t) ....(2)
differentiating equation (2) for a
a(t) = - 77.76 * cos(7.4 * t)
b)
the amplitude is 1.42 m
c)
the frequency , f = w/2pi
f = 7.4 /2pi
f = 1.18 Hz
d)
the total energy , TE = 0.5 * m * vm^2
TE = 0.5 * m * ( A * w)^2
TE = 0.5 * 0.1 * ( 1.42 * 7.4)^2
TE = 5.52 J
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