The distance between two consecutive nodes and the amplitude after 0.56s are m/2 and 1.75×10^(-4) m respectively.
<h3>What's the distance between consecutive nodes of the displacement of air molecules?</h3>
- Wavelength is the distance between two consecutive nodes or toughs or crests or anti-nodes.
- So, distance between consecutive nodes = wavelength = 2π÷k
= 2π/(4π÷m)
= m/2
<h3>What's the amplitude after 0.56s of the displacement of air molecules?</h3>
Displacement after 0.56 s = 0.008×cos(50π×0.56s)
=1.75×10^(-4) m
Thus, we can conclude that the distance between consecutive nodes and displacement after 0.56 s are m/2 and 1.75×10^(-4) m respectively.
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Question: The particle displacement y of air molecules due to a sound wave is given by y=0.008coswtsinkz where k=4π÷m and w=50π rads/s.
Calculate:
I) the distance between 2 consecutive nodes
ii) the amplitude after 0.565s
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Answer:
Part 1) Time of travel equals 61 seconds
Part 2) Maximum speed equals 39.66 m/s.
Explanation:
The final speed of the train when it completes half of it's journey is given by third equation of kinematics as

where
'v' is the final speed
'u' is initial speed
'a' is acceleration of the body
's' is the distance covered
Applying the given values we get

Now the time taken to attain the above velocity can be calculated by the first equation of kinematics as

Since the deceleration is same as acceleration hence the time to stop in the same distance shall be equal to the time taken to accelerate the first half of distance
Thus total time of journey equals
Part b)
the maximum speed is reached at the point when the train ends it's acceleration thus the maximum speed reached by the train equals 
Answer:
15.07 ksi
Explanation:
Given that:
Pitch (P) = 5 teeth/in
Pressure angle (
) = 20°
Pinion speed (
) = 2000 rev/min
Power (H) = 30 hp
Teeth on gear (
) = 50
Teeth on pinion (
) = 20
Face width (F) = 1 in
Let us first determine the diameter (d) of the pinion.
Diameter (d) =
=
= 4 in
From the values of Lewis Form Factor Y for (
) = 20 ; at 20°
Y = 0.321
To find the velocity (V); we use the formula:


V = 2094.40 ft/min
For cut or milled profile; the velocity factor
can be determined as follows:


= 2.0472
However, there is need to get the value of the tangential load
, in order to achieve that, we have the following expression




Finally, the bending stress is calculated via the formula:



15.07 ksi
∴ The estimate of the bending stress = 15.07 ksi