Darin is traveling on a spaceship moving away from earth at a velocity of 30,000 km/sec. just when he reaches a distance of 100 aui (in earth coordinate system), katia on earth sends him a radio signal at frequency 2.5 ghz. immediately after receiving the signal darin’s radio transmits a response at the same frequency it was received.

(a) how long (in hours) after katia’s transmission does the return signal arrive?

(b) what frequency (in ghz) does darin measure for the incoming signal?

(c) what frequency (in ghz) does katia measure for the return signal?

(d) by what fractional amount does the exact relativistic kinetic energy of the spaceship differ from the newtonian value?

(e) repeat part (d) but this time obtain it by expanding the relativistic expression for kinetic energy to order β 4.

(f) for what value of β is the fractional error 10%?

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 ⇒

If a tank filled with water contains a block and the height of the water above point a within the block is 0.8 meter, what is the pressure at point a?

For which pair of objects would adding the same a