Teacher having experience more than 5 years as a teacher for K-12.
By explicit differentiation, check that the functions $f_{1}, f_{2},$ and $f_{3}$ in the text satisfy the wave equation. Show that $f_{4}$ and $f_{5}$ do not.
Show that the standing wave $f(z, t)=A \sin (k z) \cos (k v t)$ satisfies the wave equation, and express it as the sum of a wave traveling to the left and a wave traveling to the right (Eq. 9.6).
Use Eq. 9.19 to determine $A_{3}$ and $\delta_{3}$ in terms of $A_{1}, A_{2}, \delta_{1},$ and $\delta_{2}$.
Obtain Eq. 9.20 directly from the wave equation, by separation of variables.
Suppose you send an incident wave of specified shape, $g_{I}\left(z-v_{1} t\right),$ down string number $1 .$ It gives rise to a reflected wave, $h_{R}\left(z+v_{1} t\right),$ and a transmitted wave, $g_{T}\left(z-v_{2} t\right)$. By imposing the boundary conditions 9.26 and $9.27,$ find $h_{R}$ and $g_{T}$.
Jack drops a stone from rest off of the top of a bridge thatis 20.0 m above the ground. After the stonefalls 6.6 m, Jill throws a second stone straight down.Both rocks hit the water at the exact same time. What was theinitial velocity of Jill's rock? Assume upward is the positivedirection and downward is negative. (Indicate the direction withthe sign of your answer.)
Calculate the electrostatic field intensity and potential midwaybetween two points charges in air, one of +300 statC and the otherof -100 statC. What work would be required to bring a charge of+19.5 statC from a very distant point to this point?
It is desired to manufacture a uniform wire from M = 5.0 g of ametallic material that obeys the Ohm law and whose density isρm = 12.5 g / cm3. After having built it, using all the material,it is found that the electrical resistance of the wire is R = 10.5Ω, that its length is L = 15.6 m; What is the resistivity ofunknown material in SI units?
When a solid undergoes a phase transition, the volume change is independent of the pressure, ΔV = 1.0 cm³/mol. Now, when the pressure is increased from 1.0 bar to 3.0 Mbar, calculate the change in the Gibbs energy of the phase transition. (1 bar = 10⁵ Pa)
Consider a linear chain of atoms with length L. Along thischain both longitudinal and transverse waves can propagate. The velocity of Longitudinal waves is vl and thatof transverse waves is vt. Apply the Debye modelto the system and find the density of states g(ω) as a function ofthe frequency ω of the phonons. Next, write down anexpression for the Debye frequency in terms of the number of atomsper unit length (N/L).
#7. A vessel whose walls are thermally insulated contains 2.70 kg of water and 0.460 kg of ice, all at a temperature of 0.0 °C. The outlet of a tube leading from a boiler in which water is boiling at atmospheric pressure is inserted into the water. How many grams of steam must condense inside the vessel (also at atmospheric pressure) to raise the temperature of the system to 27.0 °C? Neglect the heat transferred to the container.
