Here is a summary of what we covered in the two midterm review sessions. * You must put all basic knowledge in your mind (not in cribsheet). * The exam is just one way to show your knowledge. If you mess up in an exam, you have other chances to show your knowledge (extra credit reports; good reports can be written even on very basic stuff that everyone is supposed to know very well). Here are some specific physics related things that we went over. <> Here, we have two topics. First (the upper part), the energy contained in a sinusoidal wave is given by the circled expression. If it is a traveling sinusoidal wave, then it is dead easy to integrate this experssion, since $\int dm = M$ for a segment of wave medium of length $L$ and mass $M$. If it is a standing sinusoidal wave, the integral is not as trivial, since $A$ is $x$ dependent. Second (the lower part), a spherical wave is locally a plane wave, whose intensity is proportional to $A^2$. Since the intensity of a spherical wave $\propto 1/r^2$ by energy conservation, we then see that $A \propto 1/r$ for a spherical wave. In the following two photos, key elements for problem 7 are listed. They are (1) $f$ is determined by the tuning fork and remains unchanged whether the surrounding gas is air or He, (2) $\lambda_{He}$ of the sound wave in He is three times of $\lambda_{air}$, since $v_{He} = 3 v_{air}$, and (3) the resonance condition $\lambda = 4L (2n + 1)$. (Note that $m$ and $n$ are related.) You must use these facts to arrive at a good resolution of the problem! <><><> <><><> In the following two photos, the key elements for problem 6 are listed. Note that many details are left out for your complete work. <><><> <><><> This photo sketches how to approach the problem related to the measurement of the depth of a well through the measurement of the sound coming back from a stone dropped in the well. Note that a quadratic equation for $x = \sqrt{d}$ must be solved. <><><> This image shows a simple Doppler effect example. <><><> In this photo, it is illustrated how to determine the signs in a Doppler effect problem when both source and observer are moving. Note that both cars are moving, while in (1) or (2) we are deliberately, and temporarily, setting one of the speeds to be zero, in order to determine the sign for the Doppler effect formula. <><><> Here is the problem of a child not hearing Mom. This problem is very analogous to the two speaker problem. Calculate $(x_2 - x_1) / \lambda$ and you should get a good answer as to whether the child has a point or not. <><><> Here is the solution to part (b) of the two speaker problem. Note that in reality the zero intensity would not be possible. So, the "noise level" decibel may be the more practical answer. Note also that, since $I_0$ is the threshold of human ear, negative decibels are perfectly acceptable since there are intensity levels human ears are not sensitive to but other animals or instruments are sensitive to. <><><> This image may be a bit misleading. Note: part (a) constructive interference, part (b) '''destructive interference''' (total phase difference between the two paths is $\pi$, solely due to the phase shifting at one speaker, because geometry-wise the two paths are totally symmetric).