In which order did the events forming our solar system occur? the solar nebula flattened into a rotating disk. as gas became hot and dense, it spun faster and faster and was pulled toward the center, forming the sun. gas was pulled toward the center, forming the sun. gas flattened into a rotating disk and became hot and dense, forming a solar nebula that spun faster and faster. gas flattened into a rotating disk and became hot and dense, forming a solar nebula that spun faster and faster. gas was pulled toward the center, forming the sun. the solar nebula spun faster and faster and flattened into a rotating disk. most of the gas was pulled toward the center, where it became hot and dense, forming the sun.

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒