A transverse harmonic wave travels on a rope according to the following expressi
ID: 1473958 • Letter: A
Question
A transverse harmonic wave travels on a rope according to the following expression:
y(x,t) = 0.14sin(2.1x + 17.8t)
The mass density of the rope is = 0.105 kg/m. x and y are measured in meters and t in seconds.
1)
What is the amplitude of the wave?
m
2)
What is the frequency of oscillation of the wave?
Hz
3)
What is the wavelength of the wave?
m
Your submissions:
4)
What is the speed of the wave?
m/s
Your submissions:
5)
What is the tension in the rope?
N
Your submissions:
6)
At x = 3.4 m and t = 0.48 s, what is the velocity of the rope? (watch your sign)
I got -2.49m/s for this and its correct.
7)
At x = 3.4 m and t = 0.48 s, what is the acceleration of the rope? (watch your sign)
m/s2
8)
What is the average speed of the rope during one complete oscillation of the rope?
m/s
Explanation / Answer
Here ,
y = A* sin(k * x + w * t)
y(x,t) = 0.14sin(2.1x + 17.8t)
comparing the equations
1)
amplitude of the wave = A
amplitude of the wave = 0.14 m
2)
comaping , w = 17.8 rad/s
frequency of oscillation = w/2pi
frequency of oscillation = 17.8/6.282
frequency of oscillation =2.833 Hz
3)
wavelength = 2pi/k
wavelength = 2pi/2.1
wavelength = 2.99 m
the wavelength of wave is 2.99 m
4)
speed of wave = frequency * wavelength
speed of wave = 2.833 * 2.99
speed of wave = 8.47 m/s
the speed of wave is 8.47 m/s
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