what is the net force if you push a cart to the right with 5N of force and a friend pushes the cart to the left with 5N of force
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To solve this problem it is necessary to apply the concepts related to wavelength depending on the frequency and speed. Mathematically, the wavelength can be expressed as
Where,
v = Velocity
f = Frequency,
Our values are given as
L = 3.6m
v= 192m/s
f= 320Hz
Replacing we have that
The total number of 'wavelengths' that will be in the string will be subject to the total length over the size of each of these undulations, that is,
Therefore the number of wavelengths of the wave fit on the string is 6.
We know that arc length (x(t)) is given with the following formula:
Where r is the radius of the barrel. We must keep in mind that as barrel rolls its radius decreases because less and less tape is left on it.
If we say that the thickness of the tape is D then with every full circle our radius shrinks by d. We can write this down mathematically:
When we plug this back into the first equation we get:
We must solve this quadratic equation.
The final solution is:
It is rather complicated solution. If we asume that the tape has no thickness we get simply:
Where r is the radius of the barrel. We must keep in mind that as barrel rolls its radius decreases because less and less tape is left on it.
If we say that the thickness of the tape is D then with every full circle our radius shrinks by d. We can write this down mathematically:
When we plug this back into the first equation we get:
We must solve this quadratic equation.
The final solution is:
It is rather complicated solution. If we asume that the tape has no thickness we get simply: