Review: Oscillations and Waves

LECTURE 12

Identify Setup Execute EvaluateIDENTIFY Identify what the question asking Identify the known and unknown physical quantities (units) SETUP need a good knowledge base (memory + understanding) Visualise the physical situation Diagrams - reference frames / coordination system / origin / directions Write down key concepts, principles, equations, assumptions that may be needed to answer the question

EXECUTE Answer to the question from what you know. Numerical questions - solve before calculations - manipulate equations then substitute numbers add comments. EVALUATE CHECK - answer reasonable, assumptions, units, signs, significant figures, look at limiting cases

Q12.1

The period of a SHM oscillator is independent of its

A frequency

B amplitude

C force constant

D mass

Q12.2

An object undergoes SHM. Its maximum speed occurs when its displacement from its equilibrium position is

A zero

B a maximum

C half its maximum value

D quarter of its maximum value

Q12.3

In SHM, there is always a constant ratio between the displacement of the mass and the

A velocity

B acceleration

C period

D spring constant

Q12.4

An object attached to a horizontal spring executes SHM on a frictionless surface. The ratio between its kinetic energy when it passes through the equilibrium position and its potential energy when the spring is fully extended is

A less than 1

B equal to 1

C more than 1

D equal to the ratio between its mass and the spring constant

Q12.5

The period of a spring / mass system depends upon the

A mass only

B amplitude

C spring constant only

D total energy

E ratio mass / spring constant

Q12.6

The amplitude of an object undergoing SHM is

A the total range of the motion

B its maximum displacement either side of the equilibrium position

C number of cycles per second it describes

D dependent upon the period of the motion

E equal to the minimum displacement from the equilibrium position

Problem 12.1

An ultrasonic wave at 8.000104 Hz is emitted into a vein where

the speed of sound is about 1.5 km.s-1. The wave reflects off the red

blood cells moving towards the stationary receiver. If the frequency

of the returning signal is 8.002104 Hz, what is the speed of the

blood flow?

What would be the beat frequency detected and the beat period?

Draw a diagram showing the beat pattern and indicate the beat

period.

[Ans: 0.19 m.s-1]

Problem 12.2

Describe the motion of a bungee jump in terms of the key physical principles.

(1) Assume no dissipative forces

(2) Assume non-zero dissipative forces

Problem 12.3A simple apparatus for demonstrating resonance in an air column is using a tuning fork and a hollow pipe which is moved up and down in the water to locate the resonance frequencies.

The smallest value of L for which a peak occurs in the sound intensity is 90.0 mm.

What is the frequency of the tuning fork?

The value of L for the next two resonance frequencies?

Speed of sound in air, v = 343 m.s-1

[Ans: 953 Hz, 0.270 m 0.450 m]

L

Problem 12.4

Oil (n = 1.20) leaking from a damaged tanker creates a large oil slick on the

harbour (n = 1.33). In order to determine the thickness of the oil slick, a plane is

flown when the Sun is overhead. The sunlight reflected directly below the plane

is found to have intensity maxima at 450 nm and 600 nm, and no wavelengths in

between. What is the thickness of the oil slick?

[Ans 750 nm]

PHYS 1002 Exam, 2002Q11c

In air (n = 1.00) light is incident normally on a thin film with an index of refraction n = 1.25. The film covers a glass lens of refractive index 1.45. What is the minimum thickness of the film to minimise reflection of blue light (400 nm)?

1

dthin film

1 n f n2

n f

(a) Explain the meaning of the concepts of constructive and destructive interference when applied to two monochromatic waves. You can draw diagrams showing the waves produced by two sources as part of your answer.

(b) When light reflects off a surface it can have zero change in phase or a change in phase. What is the significance of the refractive index in determining this change upon reflection?

(c) A fused silica lens of refractive index 1.46 is surrounded by air. Explain why a ‘quarter wavelength’ thick magnesium fluoride (refractive index of 1.38) coating over the front surface of the lens can reduce reflections and hence increase the amount of light transmitted through the lens.

(d) Light from a helium neon laser (wavelength 633 nm) is normally incident upon the coated lens described in part (c). What is the minimum thickness of the film that will result in minimum reflected intensity

PHYS 1002 Exam, 2004 - Question 12

Soap film fringes illuminated by white light

Why does the film look dark at the top (where it is thinnest)

Workshop Tutorial 12: Waves, Quantitative Question c, d, e

A source with a frequency of 5.00x106 Hz is used to measure a patients blood flow rate. The speed of sound in blood is 1570 m.s-1. The changes in frequency are some so ignore the usual rules for significant figures and quote your answers to an integer number of Hz

c. If the blood flow is away from the machine at 20 mm.s-1, what will be the frequency received by the cells?

d. What will the frequency received by the detector in the ultrasound machine?

e. Given this average blood velocity, how is it possible that the pulse pressure wave

produced by the heart reaches the feet in less tan 1 s?

Doppler effect

Doppler effectFrom formula sheet:

fo vvovvs

f s

c. If the blood flow is away from the machine at 20 mm.s-1, what will be the frequency received by the cells?

For this part what quantities do we know?

What are we trying to find?

How do we know which signs to use?

[4999936 Hz]

Doppler effectFrom formula sheet:

fo vvovvs

f s

d. What will the frequency received by the detector in the ultrasound machine?

For this part what quantities do we know?

What are we trying to find?

How do we know which signs to use?

[4999872 Hz, ie. f = -130 Hz]

SHM

a 2x

extra

v 2 xmax2 2 sin2 t

xmax2 2(1 cos2 t )

2(xmax2 x 2)

v (xmax2 x 2)

acceleration is 180 out of phase with displacement

At extremes of oscillations, v = 0

When passing through equilibrium, v is a maximum

SHM and energy

PE 1

2kx2 1

2kxmax

2 cos2t

KE 1

2mv 2

1

2mxmax

2 2 sin2t 1

2kxmax

2 sin2t

E total KE PE 1

2kxmax

2 costant

extra

how did I get this?

how do PE and KE vary during an oscillation?