Question 1:
On a hot summer's day, you are lazing at the beach with you friends, watching the ebb and flow of the waves, when you decide to try to determine some of the wave parameters.
You grab your smartphone and using the inbuilt stopwatch app and a new physics app, you are able to determine the following:
- The equivalent of 9 full sine waves pass a particular point on the shore per minute.
- The average height of the waves from crest to trough is 1.2 m.
- From a particular point on the shore, a wave moves a distance of 300 metres in one minute.
a) What is the amplitude and wavelength of the waves?
b) If the height of the waves is halved, what will be the wavelength?
c) If the velocity of the waves is doubled, what will be the frequency of the waves?
Question 2:
You decide to give each of your parents a thin platinum ring as a gift on their 50th wedding anniversary. Your parents live overseas so you want to post these rings to them via courier and have the following information:
- Combined volume of the two rings is 1.051 cm3
- Density of platinum is ρ = 21450 kg/m3
- Mass of the ring box is 112 g (one box for both rings)
- Cost of premium courier service (with security) is $AU200.00/kg
a) What is the weight of the rings and box combined?
b) How much is it going to cost you to post the rings overseas?
c) If the rings were made out of a different metal, say silver, would it cost you less to post the rings? If so, how much would the same rings in silver cost to post?
Question 3:
The company you work for has been contracted to design the light show for a rock concert. You have been tasked to work on this project and as such begin by investigating the behaviour of lasers.
There is a 95 mW laser which produces 650 nm red light; a 80 mW laser which produces 632.8 nm orange light; a 75 mW laser that produces 532 nm green light; an 85 mW laser that produces 488 nm blue light; and a 65 mW laser which produces 434nm violet light.
a) What is the correlation between the wattage and the colour of the lasers?
b) In terms of wavelength, what is the significance of the different colours?
c) Is there a relationship between the energy of a photon and a certain colour?
d) Do the different colours of lasers affect the velocity of the laser light?
e) What is the number of photons the blue light emits each second?
f) What is the number of photons the red light emits each second?
g) Compare and discuss in brief detail the results you obtain for the number of photons in blue and red light.
Note: Take Planck's Constant, h = 6.63 × 10-34 J-s and the speed of light, c = 2.99792458 × 108 m/s.
Question 4:
Your client is the curator of the local museum and as such is responsible for the way the various objects are displayed. Usually, the items are displayed inside the large, clear Poly(methyl methacrylate) (PMMA) display cabinets which are already installed in the museum, however, your client recently received a rare collection of butterflies which are housed in their own Polyethylene terephthalate (PET) glass case and she is considering which is the best way to display this item.
Does she:
(i) Leave the butter collection in its glass case and display this as is on top of a stand?
(ii) Remove the butterfly collection from its case and place the collection inside the existing large display cabinet?
(iii) Leave the display in its glass case and place this inside the existing large display cabinet, in which case visitors would be looking at the butterfly collection through two layers of glass?
In order to assist your client in making this decision, you do some thinking and quick calculations.
a) In relation to visitors' ability to see the collection under the glass, what is the significance of the two different refractive indices? Explain in detail.
b) Presuming the butterfly case is placed inside the museum display cabinet (as per Option (iii)), what is the critical angle for light passing through the two layers of glass?
c) If the situation was reversed, and the butterfly case was made of PMMA and the museum display cabinet was made of PET, what would be the critical angle for light passing through the two layers of glass? Again, assume the butterfly case is placed inside the museum display cabinet.
d) After careful exploration of the situation and based on the above considerations, which option would you recommend your client select? Explain in detail.
Take the refractive index of the PET butterfly case to be 1.5750 and the refractive index of the existing PMMA museum display cabinets to be 1.4893.
Question 5:
A rectangular glass block (n = 1.47) lies submerged at the bottom of a tank of water. A light beam enters the water from the air above, making a 35° angle to the normal in the air.
Determine the angle the light ray makes with the normal in the:
(a) Water
(b) Glass
The Refractive Index of air is 1.00 and that of water is 1.33.
Question 6:
On a recent hike with a friend through hilly country, you decide to test the acoustics of the cliffs around you. Looking at your map, directly north of your position, you see a 250 m high cliff called Buzzard's Rest that is ≈ 177 m away. Looking due east, you see a 420 m escarpment called Owl's Perch that is ≈ 364 m away. Due west is an 83 m high bluff called Traveller's Stand that is ≈ 470 m away; and, due south is a 720 m ridge called Hawk's Eye that is ≈ 893 m away.
The temperature at this time of the day is ≈ 25°C. From your interests in drone flying and acoustics, you recall the formulas for the speed of sound in air and wave motion, and using this knowledge you begin to determine the following:
a) Write down the formula and determine the speed of sound in the air at this temperature.
b) Disregarding the echo from the other directions, if you face Buzzard's Rest and shout, how long will it take for you to hear the echo?
c) Similarly, if you face Owl's Perch, Traveller's Stand, and Hawk's Eye, respectively, how long will it be until you hear an echo from each specific direction?
d) Which location will take the least amount of time for you to hear an echo? Explain in detail why this is the case.
e) If the ambient temperature was colder, say 10°C:
(i) What would be the speed of sound in the air?
(ii) Would a temperature of 10°C make a difference to the time it takes for you to hear an echo in each direction? If there is a difference, what is the difference as a percentage? If there is no difference then why is this the case? Explain your reasoning and provide the example if you were facing south.
f) Which is the most critical factor(s): the geographical direction, the air temperature, the distance to the object which the sound is bouncing off, or the height of the object which the sound is bouncing off? Or, alternatively, is there another parameter(s) that is even more important?