Physics 112 – Test #5
30 November 2016
Name ______
Directions: This is a CLOSED BOOK test, and you may only use the calculator and cheat sheet provided. SHOW ALL OF YOUR REASONING! You can only get partial credit for an incorrect answer if you show your reasoning. You may have as much time as you like to finish this exam.
1. A very light string (μ = 0.2 g/m) is connected seamlessly (i.e., no knots) to a heavy rope (μ = 217.8 g/m) so that the tension in both is the same. A pulse travels down the light string towards the point where they are connected as shown below.
a) (5 pts) Draw what the above looks like shortly after the pulse gets to the junction between the two ropes.
b) (x pts) What is the ratio of the speed of the pulse on the heavy rope to that on the light rope? (A numerical answer is expected.)
2. An infinite transverse sinusoidal wave traveling in the negative x direction on a horizontal string has an amplitude of 4.0 cm, a wavelength of 53.0 cm, and a frequency of 211 Hz. The vertical displacement of the string at t = 0 and x = 0 is +1.0 cm. Assume the wave’s mathematical formula has the form yx, t=Asin(kx±ωt±δ).
a) (10 pts) Determine the phase constant of the wave.
b) (10 pts) Write out Asin(kx±ωt±δ) with the correct numbers filled in for A, k, ω, and δ, and with the correct signs filled in for the ±’s.
c) (5 pts) What is the maximum transverse acceleration of the piece of string at x = 6.67 cm?
3. A tuba acoustically behaves like a tube open at both ends (at least for the purposes of this problem). The lowest note on you can play on a tuba (a Bb1 or 58.27 Hz) is actually the resonant frequency that has two pressure antinodes in the instrument’s standing wave.
a) (10 points) Calculate the uncoiled length of the tube that makes up a tuba when it plays this note.
b) (5 points) If a tuba goes sharp (e.g., its 110 Hz note comes out 115 Hz), how would one fix this? Why, physically, does your solution work?
4. (15 pts) Two speakers hang from a very high ceiling, one 12 meters higher than the other. They emit a single frequency in phase. A man stands 9 m to the left of the lower speaker so that his ears are at the same height as the speaker, as shown. The volume sounds particularly soft to the man. He walks towards the lower speaker, and when he is 5 m away from it, the volume again sounds soft. (The sound does not sound soft in between these two distances.) Determine the frequency emitted by the speakers. You may assume that the speed of sound is 345 m/s.
5. (15 pts) A salesperson claims that a certain speaker delivers 20W of audio power. Testing the system, a consumer noticed that she could get as close as 1.1 m from one speaker with the volume full on before the sound hurt her ears (120 dB, the threshold of pain). Is the salesperson correct? You may assume that the speaker is a point source and that it radiates sound out evenly over half a sphere.
6. (13 pts) Consider a string of length L that is clamped at both ends. (Each end is connected to a ring of negligible mass that is free to slide up and down a rod without friction.) The speed of waves on this string is v. Someone’s finger will lightly touch the string at a point ¼ the way along the string, forcing a node there. Derive a formula for the frequencies that will form standing waves on this string. Your expression may contain only v, L, n (an integer), and pure numbers (like 2, π, etc.).
7. (xx pts) An alien is taking a walk on the planet Zorxflap. The air on Zorxflap is cold and dense enough that the speed of sound here is only 60 m/s (all speeds given here are relative to the ground). A stiff wind blows to the left at 40 m/s. The alien walks with the wind at a speed of 5 m/s. A space pirate goes by the alien with a speed v while yelling (singing?) “Yaaarrrrr” at a particular frequency. As he approaches the alien, the frequency the alien hears him singing at is 2000 Hz. After he goes by the alien, the frequency the alien hears is 330.4 Hz (7600/23 Hz). Determine how fast the pirate is moving relative to the ground AND the frequency he’s singing (what frequency the alien would hear if there was no wind and neither the alien nor the pirate are moving).
BONUS BRAIN BUSTER!!! (+5 points) A bullet travels horizontally to the right. Of course, it, like most bullets, travels faster than the speed of sound, creating a small shock wave in its wake as shown in the picture. The shock wave makes an angle of 31o with respect to the horizontal. Calculate the speed of the bullet based on this information.
Other pictures of shock waves:
Credit will only be given for correct reasoning. If you are able to guess the correct answer but give no correct reasoning, you will receive no extra credit. However, if you give some correct reasoning that would (or does) lead to the correct answer, at least some credit will be given.
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By signing my name above, I affirm that this test represents my work only, without aid from outside sources. In all aspects of this course I perform with honor and integrity.