Base Quantity and Derived Quantity

(Reviewed and updated on 30/05/2016)

Quality and Quantity

1.      Quality refers to a non-quantitative characteristic of a matter or phenomenon that can be described. For examples: inverted or upright; virtual or real; red, green, blue, etc.; opaque or transparent; sweet, salty, sour or bitter; etc.

2.      Quantity:

·        Quantity refers to a characteristic of a matter or phenomenon that can be quantified. To quantify means to measure and give it a numerical value and a unit of measurement.

·        A unit of measurement indicates the size of that unit based on a measurement standard and together with the numerical value, they express the size of the physical quantity.

·        Examples of physical quantities:

o       Mass, weight

o       Length, area, volume

o       Time

o       Temperature

o       Electric current, voltage, resistance, charge

o       Number of particles in a matter

o       Brightness of light

o       Angle (of reflection, refraction…), etc.

·        In the past, for the same physical quantity, different units of measurement were used depending on the cultural backgrounds of the users. For examples:

o       For mass: kilograms, tonnes, pounds, ounces, grams…

o       For length: inches, feet, millimeters, centimeter, metres, etc.

o       For time: seconds, minutes, hours, days, etc.

o       For temperature: Celsius (or Centigrades), Fahrenheits, kelvins

This has caused difficulty in comparison and communication.

·        To overcome the difficulty, the SI (International System of Units) has chosen and standardized the units of measurement for all physical quantities – and, these chosen units of measurement are known as the SI units.

·        SI has recognized some physical quantities as base quantities and others as derived quantities. What are their differences?

Base Quantities & Base Units

1.      Base quantities are fundamental physical quantities that are not defined in terms of other physical quantities and upon which other physical quantities - known as derived quantities - are derived. The following physical quantities, units and symbols are chosen by the SI (International System of Units) as base quantities, base units and unit symbols:

Base Quantity (Symbol)                  Base Unit (Symbol)

Length (l)                                        metre (m)

Mass (m)                                        kilogram (kg)

Time (t)                                          second (s)

Electric current (I)                       ampere (A)  (2013 P1 Q1)

Temperature (T)                             kelvin (K)

      (2006 P1 Q1 Pg. 48)
   
2.      The SI has recognised 7 quantities as base quantities and defined their base units as: metre, kilogram, second, ampere, Kelvin, mole and candela.

[Students' Common Misunderstanding / Error on "Electric Current":

1) Students - because they can easily remember electric current as I = V/R (Ohm's Law) or I = Q/t (rate of flow of electric charges) - tend to think that "electric current", I is a derived quantity: This is wrong!  Electric current (I) was chosen by SI to be a base quantity - a fundamental physical quantity. A base quantity - though is not defined in terms of other quantities - can however be expressed in terms of other quantities. For example: the base quantity length (l) can be expressed in terms of "square  root of the area A of a square" and, that does not make length a derived quantity! Similarly, electric current (I) - though can be expressed in terms of I = V/R or, I = Q/t - is a base quantity as chosen by SI!

2) SI defines electric current of one ampere as the current that flows through 2 straight conductors of infinite length of negligible cross-sectional area placed 1 metre apart in vacuum that produces between the conductors a force of 2 x 10^-7 newton per metre length of the conductors]

Derived Quantities & Derived Units
  

1.      Derived quantities are physical quantities which are derived from the base quantities by multiplication or division or both. For example, speed is a derived quantity of length (distance travelled) over time.

2.      Derived units are units of measurements (for derived quantities) which are derived from base units of the component base quantities by multiplication or division or both. In the case of the derived quantity, speed, its derived unit is metre/time (with unit symbol, m/s or ms^-1).

3.      Some derived units have been given special names by SI. For examples:

Derived Quantity (Symbol) Formula            Derived Unit (Special Name)

·        Force (F)                     Mass x Acceleration     kg ms^-2 (newton, N)

·        Pressure (P)                 Force/Area                   kg ms^-2/m² (pascal, Pa)

·        Frequency (f)                1/Period                       1/s = s^-1 (hertz, Hz)

·        Work (W)                    Force x Displacemt       N x m (joule, J)

·        Power (P)                    Work/Time                   J/s (watt, W)  
Electric charge (Q)        Current x Time                A s (coulomb, C)

(2011 P1 Q3 at pg. 280 - Weight being a measure of gravitational force is a derived quantity
2012 P1 at pg. 332 - What is the S.I. unit for density? Answer: D kg m^-3 - avoid C) 

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Segment Review Questions:

A)  Base Quantity and Derived Quantity

1.    What is a base quantity? Name 5 base quantities.

2.    Define derived quantity. And, state 5 derived quantities.

3.    State two main advantages of standardization of all units of measurement for physical quantities.

4.    Give the name and symbol of the SI unit of measurement for each of the following physical quantities:

a.       Length

b.      Mass

c.       Time

d.      Temperature

e.       Current

f.        Force

g.       Energy

h.       Power

5.    Some derived quantities have been given special names by SI (International System of Units). State these derived quantities (that you know of) and their special names.

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Reviewed and updated on 30/05/2016 by tutortan1@gmail.com
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Summary - SPM Past Year Questions on "Intro To Physics"

Summary - SPM Past Year Questions - “Intro. To Physics” (F4 Chap. 1):

Year	Paper 1 (50 Qs) (1hr 15min)	Paper 2 (2hr 30min) A: 8 Qs – Do All (90 min, 60 pts) B: 2 Qs – Do 1Q (30 min, 20 pts) C: 2 Qs – Do 1Q (30 min, 20 pts)	Paper 3 (1hr 30min) A: 2 Qs (28 pts) (advice: 1 hr) B: 2 Qs – Do 1Q (30 min, 12 pts)
2011	Q1~3 (3Qs) Pg 280	NIL	NIL
2010	Q1&2 (2Qs) Pg 230	A.Q1 (Pg 246)	A.Q1 (Pg.268)
2009	Q1~3 (3Qs) Pg 186	NIL	A.Q1 (Pg 220)
2008	Q1 (1Q) Pg 140	NIL	A. Q1 (Pg 174)
2007	Q1~3 (3Qs) Pg 92	NIL	NIL
2006	Q1~3 (3Qs) Pg 48	NIL	NIL
2005	Q1&2 (2Qs) Pg 3	A.Q1 (Pg 16)	NIL
2012	Q1~Q3 (3 Qs) Pg 332	A Q1 (Pg 346)	NIL

Interference of Waves

1. Interference of waves occurs when 2 sets of continuous waves meet and overlap and their wavefronts superimpose each other in accordance with the principle of superimposition.

2. Principle of superimposition states that: when 2 waves overlap, the resultant displacement is equal to the sum of displacement of the 2 individual waves.

3. Effects of Interference:

• Change in amplitude:

• Constructive interference produces maximum amplitude (max. crest or trough) at points of antinodes; Lines that join points of antinodes are known as antinodal lines.

• Destructive interference produces zero amplitude at points of nodes. Lines that join nodes are known as nodal lines. 

• No change in: Frequency ( f), wavelength (λ) and speed (v) IF the waves are from coherent wave sources:
• Coherent waves are waves which maintain a constant phase difference and can be produced by 2 oscillating sources vibrating at the same frequency.

4. Overlapping waves interfere either constructively or destructively:

• Constructive Interference: When 2 waves meet with the same amplitude in the same direction (e.g. crest meets crest or trough meets trough), the resultant displacement is the combination of the 2 amplitudes in the same direction (e.g. higher crest or deeper trough of double amplitude) - this is known as constructive interference.

• Destructive Interference: When 2 waves meet with the same amplitude in opposite directions, they cancel each other out - the resultant displacement is zero - this is known as destructive interference.

5. Experiments Showing Interference in Waves:

• Water Waves - Ripple Tank & 2 Coherent Water Wave Sources (Fig. 1.31 at pg. 21 of F5 textbook) (SPM 2009 P3, Q2 at pg. 224) / (2011 P3, Q4 at pg. 328);
• Light Waves - Thomas Young's "Double-Slit" Experiment (Fig. 1.32 at pg. 21 of F5 textbook)(SPM 2010 P3 Q2 at pg. 273) / 

          (SPM 2010 P2 Q10(a) at pg 260) /
          (SPM Yr 2012 P1 Q33 @ pg 339);

• Sound Waves - Common Audio Signal to 2 Loud Speakers Experiment (Fig. 1.33 at pg. 22 of F5 textbook) (SPM 2009 P2 QA6 at pg 205) / (2010 P2 Q6 at pg. 253)

6. Approximate Formula for Wavelength (λ = ax/D) from Interference Pattern:

• where, λ = wavelength

                   a = distance between the 2 coherent wave sources
               
                   x = distance between 2 adjacent antinodal lines
                         (radiating ripples or interference fringes or points of loudness)

                   D = perpendicular distance between the parallel lines
                          where a and x are  measured 

• From experiment, empirical evidence shows:
• that x is directly proportional to λ
• that x is inversely proportional to a
• therefore, mathematically, x = kλ/a, where k is found to be = D
• Thus, x = Dλ/a
• And, mathematically, λ = ax/D

• Thus, the "Approximate Formula for Wavelength" can be used to find the wavelength of waves from their interference patterns. 

• From the formula λ = ax/D or x = Dλ/a (same formula with different subjects)
• Interference pattern of red, green or blue light can all be explained by the "Wavelength Approximate Formula, x = Dλ/a" 
• The distance between adjacent fringes x of red light is bigger than that of green or blue because the wavelength of red light (λ _red) is longer as compared to that of green light (λ_green) or blue light.
• Since  λ _red > λ_green > λ_blue, from  x = Dλ/a, therefore, x _red > x_green > x_blue.

• Application of Interference:
• In water waves - Spherical bow of ship produces destructive interferences to lessen resistance to movement of ship thereby saving energy;
• In sound waves - Destructive interference is used to silent engine noise in cabin of aeroplane, car and headphone (please see below)
• In light waves - Interference pattern and the "Wavelength Approximate Formula" is used to find the wavelength of waves.

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       Application of Destructive Interferenceof Sound Waves

Noise Cancellation

• Noise cancellation is a method to reduce or completely cancel out undesirable sound.
• A noise-cancellation speaker emits a sound wave of equal but opposite amplitude and same frequency with the original sound i.e. by emission of anti-phase sound waves.
• The sound waves will overlap each other in a process called destructive interference, causing the waves to cancel each other out and there would be no sound.
• The sum of the amplitudes of the waves is equal to zero.

 

Application of noise cancellation:

1. Headphone - people working near aircraft or in noisy factories can now wear these electronic noise cancellation headsets to protect their hearing.
2. Cars - The way it works is that a microphone connected to the car stereo system picks up all the sound inside the car, including music or such from the stereo. Then the noise-cancellation system produces noise-canceling sound waves that match the frequency of unwanted sound.
3. Aircraft - The system uses microphones to pick up the vibrations due to jet's engine in the cabin walls. It then analyzes the signals and generates counter vibrations in the walls to produce a net result of zero vibrations.

Diffraction of Waves

DIFFRACTION OF WAVES

1. Diffraction refers to the spreading out of waves as they move through a gap or bend around an obstacle about the size of the wavelength or smaller. If the size (of the gap, aperture or obstacle) is significantly larger than the wavelength, the effects of diffraction would not be obvious.

2. Effects of Diffraction:

• No change in: frequency (f), wavelength (λ) and speed (v) of the waves; and

• Change in: direction and amplitude a of the waves upon diffraction. (Amplitude of diffracted waves < amplitude of incident waves; and direction of propagation changes and the waves spread out)

3. Experimental Evidence of Diffraction:

• Water waves:
• Through Slit - Ripple Tank & Metal Bars of Different Slit Sizes
• Through Obstacle - Ripple Tank & Metal Bars of Different Sizes as Obstacles.

• Light waves (wavelength about 10^-6 or 1 micrometer):
• Narrow Slit Experiment and the Diffraction Pattern

• Audible sound waves (wavelength about 1.5cm ~ 15 m):
• Sound Heard from Hidden Corner Experiment

4. Application of Diffraction of Waves:

• In transmission and reception of radio waves because diffraction enables waves to spread to areas behind obstacles, buildings, mountains or through tunnels
• AM (Amplitude-Modulated) waves of long wavelength (186 m ~ 560 m) can spread around large obstacles like big buildings and hills
• FM (Frequency-Modulated) waves of shorter wavelength (2.6 m ~ 3.4 m) can pass through smaller obstacles like tunnels and bridges.

•  Operation of infra-red remote controls - infra- red light of even smaller wavelength compared to radio waves can be diffracted through even smaller obstacles found at home like the furniture, etc. - to turn on the TV and so on.

• Study of Atomic Structure: Diffraction of X-ray (wavelength in picometers) through atoms (atomic radius in picometers) enables scientist to study the atomic structure of a substance or chemical.

5. SPM Past Year Questions:

• 2010 P1 Q32 pg. 238
• 2008 P1 Q31 pg. 147
• 2005 P1 Q29 pg. 9 (on AM waves form (Answer: A). What if the the question asks about FM waves form? (The answer would be: C). Click here to look at both the AM and FM wave forms)

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6. Diffraction of Waves (In Very Simple Terms)

1. Diffraction is the spreading of a wave as it goes through a narrow gap or passes round a small obstacle.
2. The effect of diffraction increases when the width of the gap is decreased.



3. The effect of diffraction increases when the wavelength is increased.

Application of diffraction in sea waves

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Refraction of Waves

(Updated on 2/10/2013: to include latest SPM (2012) questions)

1. Refraction occurs when waves change direction as they enter one medium from another at an obligue angle. If a wave moves from one medium into another at right angle, there is no refraction because there is no change in direction of the wave.

2. Refraction happens because a wave moves at different speeds in different media - faster in less dense medium (or deeper water) and slower in denser medium (or shallow water).

3. The frequency of a wave in different media does not change. It is the change in wavelength that causes the wave speed to change.

     (For the above reason (24/2/2015): When a single-colour (or monochromatic) light gets refracted when it moves from one optical medium into another at an oblique angle, its wavelength changes but NOT its colour nor frequency. Hence, a monochromatic light is best described as either a single-colour light or a single-frequency light and NOT as a single-wavelength light because the wavelength can change while the colour and the frequency remain the same!)

4.  Since wave speed v = λf: when waves move from a less dense medium (or deeper water) to denser medium (or shallower water), wavelength decreases resulting in decrease in wave speed (frequency unchanged); and, conversely,  when waves move from a denser medium (or shallower water) to a less dense medium (or deeper water), wavelength increases causing the wave speed to increase. .

[Decrease in wavelength λ means successive wavefronts get closer; and, conversely, increase in wavelength (and thus wave speed) means the wavefronts get further apart]

5. When the angle of incident i of a wave as it enters another medium is zero (i.e. the direction of travel of wave is parallel to the normal or at right angle to the interface between the 2 media), there is no change in direction of the wave and therefore no refraction occurs. However, the wavelength and thus the wave speed change (since frequency remains unchanged) as its move from one medium into another medium.

6. Refraction occurs IF the angle of incident i` of the waves as they enter another medium is > zero,
   that is,  i` > 0^o:

• waves direction bends towards normal if the waves move from a less dense medium (or deeper water) to denser medium (or shallower water);

• waves direction bends away from normal if the waves move from a denser medium (or shallower water) to a less dense medium (or deeper water).

(SPM 2012 P1 Q35 @ pg 340 on characteristics of water waves undergoing refraction)

 6. Refraction of Light obeys Snell's Law: Sin i` / sin r` = n, the refractive index. (i = angle in air or vacuum, and r = angle in the other medium whichever direction the waves travel)

• Other formulae for Refractive Index n (Form 4 Chapter 5 on "Light"):
• n = sin 90` / sin c` = 1 / sin c` (where c = critical angle for total internal reflection). Note: Critical angle c and total internal reflection are always in the denser medium;
• n = Speed of Light in vacuum (or in air approximately) / Speed of Light in the medium;
• n = Real Depth (Vertical) / Apparent Depth

 
7. Natural Phenomena of Refraction: 

• Water waves: Sea wavefronts tend to take the shape of the shoreline as they approach the shore. Explanation: 
• In the centre of the ocean, the wavefronts are straight and parallel to each other because the water waves there travel at uniform speed as the depth of sea water there is almost uniform. 
• When the wavefronts approach the shoreline, they reach the headland or cape earlier than the bay because the cape represents the protruding part of the shoreline that becomes shallow earlier than the bay.
• Therefore, the water waves near the headland or cape slow down first - thus, their wavelength becomes smaller or wavefronts become closer near the cape while those approaching the bay are still having greater wavelength and their wavefronts are still further apart
• This phenomenon of refraction of water waves causes the wavefronts to take the shape of the shoreline as the waves approach the shore.

                         Refraction of Water Waves

• Water wave refraction causes wavefronts to be parallel to the shape of the coastline as they approach the shore.
• Water wave refraction also causes water wave energy to converge at cape and causing erosion - the waves at the cape are more rocky and turbulent.
• Water wave energy diverges at bay and spreads out to a wider region, causing deposition of sand, etc. The amplitude of waves at the bay is smaller than at the cape. The waves at the bay are calmer. It is safer to swim in water near the bay than near the cape. 

• Sound Waves:

• During a hot day - sound can be heard only a short distance away unlike on a cool night because:

• during daytime, air near the surface of the earth is warmer and less dense;
• while higher up, air is cooler and denser. 
• Sound is therefore refracted upwards progressively towards the normal and away from the surface of the earth:

 

• During a cool night - the opposite effect happens:
• Sound can be heard a longer horizontal distance away because 
• air is cooler and denser near the earth surface than higher up - 
• sound is refracted upwards progressively away from the normal until it is reflected back to the earth surface. (SPM 2010 P2 Q10(b) at pg. 260)
• (SPM 2012 P2 Q10(b) at pg 361)

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• Light Waves:

• Pool or tub looks shallower
• Submerged part of spoon, drinking straw or ruler looks bent
• Pencil or ruler appears broken when viewed through a glass block
• Atmospheric refraction of rising or setting sun:
• the Sun below the horizon appears above horizon;
• the Sun looks oval and flattened
• Atmospheric refraction of the stars:
• the twinkling effect
• the star appears higher than its actual position
• Divers' or fish's 96^o cone-view of the abovewater world and 42^o  view of the underwater world (assuming critical angle of the sea water being 48^o)

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(Points for discussion: Please refer Malaysian Form 5 KBSM Physics textbook:

• At pg. 36: "Refraction of waves is a phenomenon where there is a change of direction in the propagation of waves when they move from one medium to another due to a change of speed." However, a change in wave speed such when the wave enters another medium at right angle (or zero angle of incidence) does not necessarily mean a change in wave direction i.e. does not necessarily result in refraction!

• At pg 13, the 2nd paragraph on refraction: "By comparing the angle of incidence, i with angle of refraction, r in Figure 1.19, you will find that when waves travel from a denser medium to a less dense medium, they are refracted towards the normal." Shouldn't the words "towards the normal" be "away from normal"? Very serious fundamental error!

• On the above textbook error at page 13: On 10/9/2013, I tried calling the telephone number given inside the front-cover of book but found it no longer in use. So, I wrote an email to the Ministry of Education. Here are my email and the Ministry's reply. The Ministry agrees with my findings and will be taking follow-up remedial actions:

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10/9/2013

To: Whom It May Concern (azwin.milan@moe.gov.my; 03-8884 5027)

From: A Concerned Parent

Re: Significant Errors in Malaysian Form 5 Physics and Chemistry Textbooks (KBSM)

In good faith, I write to inform about what I think are significant errors in the above-mentioned Form 5 Science stream textbooks.

If the Ministry agrees that they are indeed serious errors, I sincerely hope that "Corrections Circulars" can be sent out urgently to notify all relevant parties - particularly the Form 5 Science students who will be sitting for their SPM exams. very soon. The errors:

1. Form 5 Physics Textbook (KBSM):

• At page 13: the 2nd paragraph on refraction: "By comparing the angle of incidence, i with angle of refraction, r in Figure 1.19, you will find that when waves travel from a denser medium to a less dense medium, they are refracted towards the normal." The correct underlined wordings should be "away from normal" and not "towards the normal" . This is a very serious fundamental error!

2. Form 5 Chemistry Textbook (KBSM):

• At page 188: The chemical formula for "lauryl alcohol" was given twice there as CH₃(CH₂)₉CH₂OH. The correct chemical formula for "lauryl alcohol" should be: CH₃(CH₂)₁₀CH₂OH (error highlighted in red).

I would be grateful for your follow-up actions.

Thank you.

Sincerely,

Douglas Tan

(Handphone: 011-xxxx xxxx)

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The reply from the Ministry of Education was prompt (within just 8 days) and professional: The Ministry agrees with me that there is basis to my statement that they are significant errors and that it will expeditiously carry-out follow-up actions on the errors ("Correction Circulars" to all schools throughout the country that are using the textbooks, I believe).

The Ministry's reply on 18/9/2013:
"

Ramlan Abu Talib <ramlan@moe.gov.my>	8:51 AM (6 hours ago)
to me, Pengarah, Paridin, Che, Krishnan, Syed, Sim, Wan

Malay

English

Translate message

Turn off for: Malay

En. Douglas Tan,

Tuan,

1.     Saya dengan hormatnya merujuk kepada e-mel tuan kepada Bahagian Buku Teks, Kementerian Pendidikan Malaysia,  bertarikh 10 September 2013 berhubung perkara di atas.

2.     Penyataan tuan terhadap kesilapan fakta dalam buku teks Physics Form 5 dan Chemistry Porm 5 KBSM telah dirujuk kepada Sektor Penerbitan Sekolah Menengah untuk penelitian.

3.     Setelah dibuat penelitian , pihak kami mendapati bahawa penyataan pihak tuan terhadap hal ini mempunyai asas.

4.     Pihak kami akan melaksanakan tindakan penambahbaikan dan tindakan susulan terhadap hal ini dengan segera.

5.     Pihak kami mengucapkan terima kasih di atas keprihatinan dan kerjasama tuan terhadap hal ini.

Sekian, terima kasih.

       ..Ramlan...

Ramlan bin Haji Abu Talib

b.p Pengarah

Ketua Unit Khidmat Selia

Sektor Penyeliaan dan Penyelidikan

Bahagian Buku Teks, Kementerian Pelajaran Malaysia

Aras 1-3, Blok E-15, Parcel E

62604 PUTRAJAYA

(03-88844484) ) (019-6644435) (Fax-03-88844489)

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• Posted and updated on 13/1/2015 by: tutortan1@gmail.com

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