Use the concept of beat frequency to find the applicable final freqeuncy for 20Hz beat frequency.
Beat can be defined as 'the interference pattern between two sounds of slightly different frequencies0
The expression for beat frequency is given as
Where,
Final frequency
Initial frequency
The beat frequency for us is 25Hz and the initial frequency is 240Hz, then
Being an absolute value, two values are possible, both in addition and subtraction:
The two possible values are
Answer:
The probability of finding the proton at the central 2% of the well is almost exactly 4%
Explanation:
If we solve Schrödinger's equation for the infinite square well, we find that its eigenfunctions are sinusoidal functions, in particular, the ground state is a sinusoidal function for which only half a cycle fits inside the well.
let be the well's length, the boundary conditions for the wavefunction are:
And Schrödinger's equation is:
The solution to this equation are sines and cosines, but the boundary conditions only allow for sine waves. As we pointed out, the ground state is the sine wave with the largest wavelength possible (that is, with the smallest energy).
here the leading constant is just there to normalise the wavefunction.
Now, if we know the wavefunction, we can know what the probability density function is, it is:
So in our case:
And to find the probability of finding the particle in a strip at the centre of the well of width 2% of L we only have to integrate:
If we do a substitution:
We get the integral:
This integral can be computed analytically, and it's numerical value is .0399868, that is, almost a 4% probability.
1) Displacement: -49 m, in the negative direction
Explanation:
The displacement of an object is a vector, whose magnitude is given by the difference between the final point of the motion and the starting point:
In this problem, the starting point is +34 m, while the final position is -15 m; therefore, the displacement is:
and the direction is negative, in according to the negative sign.
2) Velocity: -3.27 m/s
Explanation:
Velocity is equal to the ratio between the displacement and the time taken:
in this problem, we have:
d = -49 m is the displacement
t = 15 s is the time
therefore, the velocity is
and the direction is negative.