Angular and linear frequency of the wave

Question

Question 1: A Surfer sits on his board waiting as waves go by to catch a ride back to shore. Assuming the waves can be modelled as a sine wave given by:

h(x, t) = 1.75 sin (0.03πx - 0.15πt) [m] what is;

a) The maximum vertical movement (rise and fall) that the surfer experiences?
b) The distance between crests of the wave?
c) The angular frequency of the wave?
d) The linear frequency of the wave?
e) Assuming the rider manages to catch one of the waves how fast will they be travelling relative to the shore line?

Question 2: An undersea explosion occurs. If the sea water has density 1.03 x 10³ kg/m³ and Bulk Modulus of 2.41x10⁹ Nm^-2 ;

a) Determine the velocity of sound in sea water.

b) If the acoustic power released by the explosion is modelled as a continuous 180 kW (for the brief duration of the explosion) determine the distance that an observer would have to be from the explosion for the sound to be just at the “threshold of pain” (1 Wm^-2). You may model the distribution of sound energy as “Isotropic”.

c) Find out the sound pressure level in dB at a distance of 1 km from the explosion site.

d) Find out the change in frequency of the 50 Hz component of the explosions complex sound waveform that would be heard by an observer moving at 20 ms^-1 directly away from the site of the explosion.

Question 3: A Neutron Star is formed in the aftermath of a Supernova explosion. The star was originally rotating with a period of 20 days and had a mass of 2x10³⁰ kg and radius of 6x10⁸ m. After the explosion the star is found to be rotating with a period of 5x10^-3 s.

a) Determine the radius of the collapsed Neutron Star.
b) Determine the density of the material in the Neutron Star
c) State any simplifying assumptions you may have used in determining the above.

Question 4:

a) Explain what is meant by the term “Heat Energy”
b) An Aluminium bar 0.5m long, initially at 20 ⁰C is heated until its temperature rises by 50 ⁰C. Determine the change in length of the bar that will occur.
c) Describe what is meant by the term “Adiabatic expansion”.
d) Describe what is meant by the term “Thermal Resistance”.