Any measurement that includes both magnitude and direction
is called a(n)

Which lists the main components of darwin’s theory of evolution? a. random mutations drive evolution; the evolution of a population happens slowly; organisms have common ancestors; organisms do not change. b. natural selection drives evolution; the evolution of a population happens slowly; organisms have common ancestors; organisms change over time. c. natural selection drives evolution; the evolution of a population happens rapidly; organisms have common ancestors; organisms change over time. d. random mutations drive evolution; the evolution of a population happens rapidly; organisms have common ancestors; organisms do not change.

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 ⇒

The frequency of the fundamental of the guitar string is 320 hz. at what speed v do waves move along that string?