All categories

3 years ago

Is the displacement D(x,t)=cx2+dt2, where c and d are constants, a possible traveling wave?

1 answer:

3 0

Ok, Brainly doesn't have the required math symbols I need to give you the best looking answer so we'll have to do this the best we can. In short, yes it could be a wave. A simple wave,ψ, is described by the equation
d²ψ/dx² - (1/c²)d²ψ/dt² = 0. The right side must be a nonzero constant, which is zero here. This is a basic wave equation. It says if the second partial derivative of a function with respect to space minus the second partial derivative of that function with respect to time, multiplied by a constant (1/c² here) equals a constant (0 here) then that function describes a wave. Brainly doesn't have a partial derivative symbol so I used "d". Also the c in my equation is the speed of the wave. Not necessarily the same c as in your equation.

Now let's look at your function. The second partial derivative of it with respect to x makes the t term 0 (it's a constant as far as x is concerned) and the x term becomes 2c. Doing the same thing for the partial derivative of it for t leaves 2d. These terms represent two constants, which if subtracted, as the wave equation requires, would lead to a constant on the right, which could be made zero if the coefficients c and d are chosen correctly.

You might be interested in

You drag a suitcase of mass 8.2 kg with a force of f at an angle 41.9 ◦ with respect to the horizontal along a surface with kine

DedPeter [7]

Answer:

35.6 N

Explanation:

We can consider only the forces acting along the horizontal direction to solve the problem.

There are two forces acting along the horizontal direction:

- The horizontal component of the pushing force, which is given by

$F_x = F cos \theta$

with $\theta=41.9^{\circ}$

- The frictional force, whose magnitude is

$F_f = \mu mg$

where $\mu=0.33$ , m=8.2 kg and g=9.8 m/s^2.

The two forces have opposite directions (because the frictional force is always opposite to the motion), and their resultant must be zero, because the suitcase is moving with constant velocity (which means acceleration equals zero, so according to Newton's second law: F=ma, the net force is zero). So we can write:

$F_x - F_f=0\\F_x = F_f\\F cos \theta = \mu mg\\F=\frac{\mu mg}{cos \theta}=\frac{(0.33)(8.2 kg)(9.8 m/s^2)}{cos(41.9^{\circ})}=35.6 N$

8 0

3 years ago

Who reported four “element” classifications, but included some substances that were combinations of elements rather than true el

notsponge [240]

Antoine-Laurent Lavoisier was the first person to report the four element classification system but also ended up including some compounds rather than elements.

7 0

3 years ago

Complete the following table with the appropriate units of measurement. Word bank: gram, meter, kelvin, liter, second, grams/cm3

lara31 [8.8K]

mass gram, time sec, temp kelvin, vol liter, dens grams/cm3

5 0

4 years ago

Read 2 more answers

Two long, straight wires are separated by a distance of 9.15 cm . One wire carries a current of 2.79 A , the other carries a cur

Dafna1 [17]

Answer:

The force is the same

Explanation:

The force per meter exerted between two wires carrying a current is given by the formula

$\frac{F}{L}=\frac{\mu_0 I_1 I_2}{2\pi r}$

where

$\mu_0$ is the vacuum permeability

$I_1$ is the current in the 1st wire

$I_2$ is the current in the 2nd wire

r is the separation between the wires

In this problem

$I_1=2.79 A\\I_2=4.36 A\\r = 9.15 cm = 0.0915 m$

Substituting, we find the force per unit length on the two wires:

$\frac{F}{L}=\frac{(4\pi \cdot 10^{-7})(2.79)(4.36)}{2\pi (0.0915)}=2.66\cdot 10^{-5}N$

However, the formula is the same for the two wires: this means that the force per meter exerted on the two wires is the same.

The same conclusion comes out from Newton's third law of motion, which states that when an object A exerts a force on an object B, then object B exerts an equal and opposite force on object A (action-reaction). If we apply the law to this situation, we see that the force exerted by wire 1 on wire 2 is the same as the force exerted by wire 2 on wire 1 (however the direction is opposite).

3 0

3 years ago

I don’t know why it glitches like that???? I need help tho...brainliest for best answer

lara31 [8.8K]

Answer:

B. They each contain the same amount of matter.

Explanation:

Scientifically, mass is the amount of matter in an object.

A. Whether an object is big or small does not mean that it will be a certain mass. If you have two objects that are the same size, the denser object will have more mass, and the less dense object will have less mass.

C. The amount of space an object takes up is called the volume.

D. Different combinations and amounts of elements can give you the same mass. Rocks, books and cans of soda are made of different things.

8 0

3 years ago