Question

Like all planets, the planet Venus orbits the Sun in periodic motion and simultaneously spins about its axis. Just as on Earth, the time to make one complete orbit (i.e., the period of orbit) is what defines a year. And the time to make one complete revolution about its axis (i.e., the period of rotation) is what defines a day. The period of orbit for the Earth is 365.25 days and the period of rotation is 24 hours (1.00 day). But when these same values for Venus are expressed relative to Earth, it is found that Venus has a period of orbit of 225 days and a period of rotation of 243 days. So for Venus inhabitants, a day would last longer than a year! Determine the frequency of orbit and the frequency of rotation (in Hertz) on Venus. Ans: A marine weather station detects waves which are 9.28 meters long and 1.65 meters high and travel a distance of 50.0 meters in 21.8 seconds. Determine the speed and the frequency of these waves. Ans:

Answer 1

Answer:

a) F = 5.14 10⁻⁸ Hz,  f = 4.76 10-8 Hz,  b)   v = 2.29 m / s,   f = 42.5 Hz

Explanation:

a)This problem has two parts.

For the calculations relative to the planet Venus, we use that the period and the frequency are related

            f = 1 / T

frequency of the orbit around the Sun

   

Let's reduce the period to the SI system

           T = 225 days (24h / 1days) (3600 s / 1h) = 1.94 10⁷ s

           F = 1 / 1.94 10⁷

           F = 5.14 10⁻⁸ Hz

rotation frequency

            T = 243 d = 2.1 107 s

             f = 1 / T

             f = 1 / 2.1 107

            f = 4.76 10-8 Hz

b) give the data of some marine waves

the speed of the wave can be found with kinematics

            v = x / t

            v = 50.0 / 21.8

            v = 2.29 m / s

If the wavelength is L = 9.28m

this distance is the distance between two consecutive ridges or valleys

             λ / 2 = L

             λ = 2L

             λ = 2 9.28

             λ = 18.56 m

the speed of the wave is

             v = λ f

             f = v /λ

             f = 2.29 / 18.56

             f = 42.5 Hz