You decide to make one of the world’s largest musical instruments, using long cylindrical steel rods that are clamped tightly at both ends. The speed of longitudinal waves in rods of the type of steel you use is 5068 m/s and the steel has a Young’s modulus of 199 GPa. Required:
a. What is the density of the steel, in kilograms per cubic meter?
b. When a longitudinal wave is excited in one of the steel rods in your instrument to produce resonance, will the rod’s ends be nodes or antinodes?
c. A standard frequency for tuning musical instruments is 440 Hz for the pitch of A above middle C, denoted A4. What is the length, in meters, of the steel rod that produces the pitch A4 as its fundamental longitudinal resonance?
d. Assume, instead, that you want to create a smaller version of this, using the same kind of construction, with one rod of length 9.5 cm. What would the fundamental longitudinal resonance frequency of that rod be, in hertz, with the same longitudinal wave speed as above, 5149 m/s?

During physical science, ms. greene challenged her students to produce an energy transformation. james and jill wrapped a 4-inch nail with a coil of fifty turns of wire. they connected one end of the coil to one terminal of a knife switch. they connected the other terminal of the knife switch to the battery. finally, they connected the end of the coil to the other terminal of the battery. james held the tip of a 1-inch nail near the flat end of the 4-inch nail. jill closed the knife switch quickly and then opened it. the 1-inch nail was pulled toward the 4-inch nail. what is the best explanation of why the nail moved? a) electrical energy was converted to mechanical energy in the 1-inch nail. b) the 4-inch nail became an electromagnet and the magnetic force attracted the 1-inch nail. c) the electric current in the 4-inch nail was converted to mechanical energy in the 1-inch nail. d) the 4-inch nail had a positive charge and the 1-inch nail had a negative charge. opposites attracted.

Comedians like to joke that the reason we haven’t been visited by intelligent life from elsewhere in the universe is that aliens have been monitoring earth’s broadcasts of intellectually embarrassing tv programs, like gilligan’s island, fear factor, the jersey shore, and the jerry springer showand so consider us far too primitive to merit a visit. let’s check the assertion that aliens could have been receiving them. tv programs are broadcast at a frequency of about 100mhz with about 100kw of total power in 30frames per second, which emanatesroughly uniformly in all directions. assume that interstellar space transmits these broadcasts without attenuation. no matter how smart they are, aliens would require at least one photon per frame to interpret our signals. findthe number of photons per unit time per unit area reaching a receiver on a possible planet in the nearest star system, which is about 4 light-years away (a light-year is the distance light travels in a year). if aliens aimed a receiver or detector directly at earth, how big (in diameter) would it have to be to receive a photon per frame

Determine the maximum r-value of the polar equation r =3+3 cos 0