Light travels faster in warmer air. on a sunny day, the sun can heat a road and create a layer of hot air above it. let's model this layer as a uniform one with a sharp boundary separating it from the cooler air above. use this model to explain the formation of a mirage appearing like the shiny surface of a pool of water.

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 ⇒

On a geologic map, if the contacts between sedimentary rock units form a bull’s-eye pattern of concentric circles, with the youngest unit in the center, the underlying structure is a(n)

What are some important factors to consider when choosing a warm-up before your workout?