The frequency of the lowest standing-wave mode on a 1.0-m-long string is 20 Hz. What is the wave speed on the string?
1 answer:
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Answer:
3.28 cm
Explanation:
To solve this problem, you need to know that a magnetic field B perpendicular to the movement of a proton that moves at a velocity v will cause a Force F experimented by the particle that is orthogonal to both the velocity and the magnetic Field. When a particle experiments a Force orthogonal to its velocity, the path it will follow will be circular. The radius of said circle can be calculated using the expression:
r =
Where m is the mass of the particle, v is its velocity, q is its charge and B is the magnitude of the magnetic field.
The mass and charge of a proton are:
m = 1.67 * 10^-27 kg
q = 1.6 * 10^-19 C
So, we get that the radius r will be:
r = = 0.0328 m, or 3.28 cm.
We make a graphic of this problem to define the angle.
The angle we can calculate through triangle relation, that is,
With this function we should only calculate the derivate in function of c
That is the rate of change of .
b) At this point we need only make a substitution of 0 for c in the equation previously found.
Hence we have finally the rate of change when c=0.