MCD4160: Physics for Engineering Test 2-Oscillations & Waves Practice Test 2

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MCD4160: Physics for Engineering

Test 2-Oscillations & Waves

Practice Test 2

QUESTION 1 (4 marks)

A block with mass m = 6.0 kg is placed on top of a spring with spring constant k = 400 Nm- 1, it finds a new equilibrium point as shown in the figure below. If the block is pressed downward and released it oscillates. However, if the compression is too big the block will lose contact with the spring at the maximum vertical extension. Determine the extension at which the block loses contact with the spring. Show your working.


QUESTION 2 (4 marks)

A mass is attached to a string of length L as shown in the figure below. The hanging mass encounters a pin positioned a distance ¼L from the bottom of the string (as shown in the figure).

Determine the period of this combined pendulum (before and after hitting the pin). Provide an appropriate reason to support your answer.

QUESTION 3 (1 + 2 + 2 = 5 marks)

Two traveling waves on a long string are given by the following equations:

where y1, y2 and x are in metres and t is in seconds.

(a)     Write the equation of the resulting standing wave.

(b)     Determine the positions of the nodes of the resulting standing wave. Show your working.

(c)     Calculate the maximum transverse position of an element of the string at the position x = 0.40 m. Show your working.

QUESTION 4 (5 marks)

When an open-open end metal pipe is cut into two pieces, the lowest resonance frequency for the air column in one piece is 256 Hz and that in the other is 440 Hz. Assume the speed of the sound in the air is 330 ms- 1 .

What resonant frequency would have been produced by the original length of the pipe (before it was cut)? Show your working.

QUESTION 5 (2 + 2 + 2 = 6 marks)

A siren on a fire truck operates at a frequency off = 3000 Hz. It is moving forward (to the right in the figure) at a speed of 20 ms- 1 . The speed of sound in air is 330 ms- 1 . Determine:

(a)        The frequency of sound,f heard by the boy on the left (behind the truck).

(b)        The frequency of sound,f heard by the girl on the right (in front of the truck).

(c)        The wavelength of the wave in air moving to the left of the truck (i.e. to the rear of the truck).

QUESTION 6 (4 marks)

A screen is placed 3.0 m from a two-slit setup with the slits separated by 15 µm as shown in the figure below. The wavelength of the incident light is 400 nm. Determine the positions of the first maximum and minimum  fringes  from the principal  axis  (i.e.  from point P)  on the  screen. Assume the  small  angle approximation (sinθ ≈ tanθ). Show your working.

QUESTION 7 (2 + 2 + 2 = 6 marks)

In the following three cases (a), (b) and (c), which of the formula (A or B) provided below would you use to find the thickness (t) of a film to give an interference maximum for reflected light? Provide appropriate reason to support your answer.

(a)     Light comes from the vacuum and reflects off a soap film floating in the air.

(b)     Light comes from the vacuum and reflects off a soap film floating over glass.

(c)     Light comes from the glass and reflects off a soap film with vacuum on the other side.

QUESTION 8 (4 marks)

The figure below shows a series of three coaxial discs, which are polarizers. Suppose the transmission axes of the left and right polarizing discs are perpendicular to each other. The central disc is rotating on the common axis with an angular speed ω . Unpolarised light is incident on the left disc with an intensity Imax .

Determine the intensity of the light beam emerging from the right disc. Express your answer in terms of Imax , ω and time. You mayfind useful thefollowing trigonometric identities:


2023-05-25