2018 MJC P2 Soln

2018 MJC H2 Physics Prelim Exam Paper 2 Suggested solutions 1 (a) (i) When the system oscillates without any external periodic force applied , its frequency is called its natural frequency. Comments: Considering it is a recall question, it is poorly attempted. To get the mark, students are to mention that “it is the frequency when….” (ii) Resonance occurs when the frequency of the driving force (driving frequency) is equal to the natural frequency of the system, giving a maximum amplitude of vibration. Comments: Generally well done. However a handful of students left out the effect of resonance which is giving maximum amplitude. (b) 1) Microwave Cooking In a microwave oven, microwaves with a frequency similar to the natural frequency of vibration of water molecules are used. When food containing water molecules is placed in the oven and radiated by microwave, the water molecules resonate, absorb energy from the microwaves and get heated up. This absorbed energy then spreads through the food and cooks it. The plastic or glass containers do not heat up as much since they do not contain water molecules. 2) Radio Receiver Our air is filled with radio waves of many different frequencies which the aerial (antenna) picks up. The tuner can be adjusted so that the natural frequency of the electrical oscillations in the circuits is the same as that of the radio wave transmitted from a particular station (the desired station). The radio waves of that particular frequency cause much larger oscillations (due to resonance) resonance compared to the radio waves of other frequencies. 3) Magnetic resonance imaging Strong, electromagnetic fields of varying radio frequencies are used to cause oscillations in atomic nuclei. When resonance occurs, energy is absorbed by the molecules. By analysing the pattern of energy absorption, a computer - generated image can be produced. The advantage of MRI scanner is that no ionising radiation (as in the process of producing X-ray images) is involved. 4) Swing The swinging of the legs / the person pushing the swing has to be synchronised and at the same frequency as the natural frequency of the swing so that a large amplitude of oscillation can be obtained.

Meridian Junior College H2 Physics Paper 2 JC2 Preliminary Examinations 2018 2 5) Musical instrument Musical instruments are set into vibrational motion at their natural frequency when a person hits, strikes, strums, plucks the object. Each natural frequency of the object is associated with one of the many s tanding wave patterns by which that object could vibrate. The vibrations of the lips (brass instruments) / vibration of a wooden strip (woodwind instruments) against the mouthpiece matches one of the natural frequencies of the air column inside the brass instrument. This forces the air inside of the column into resonance vibrations. (c) 1) Earthquakes and tidal waves During an earthquake, when the frequencies of the vibration match with the natural frequencies of buildings, resonance may occur and result in serious damages. In regions of the world where earthquakes happen regularly, buildings may be built on foundations that absorb the energy of the shock waves. In this way, the vibrations are damped and the amplitude of the oscillations are lowered. 2) Vibrations in machines / metal panels If a loose part in a car rattles when the car is travelling at a certain speed, it is likely that a resonant vibration is occurring. A washing machine with an unbalanced load which has natural frequency matching the spinning frequency will get violent vibrations as resonance occurs. Place dampers in the machine / place strengthening struts across the panel or change its shape/area of panel to lower the amplitudes. 3) Suspension bridge Suspension bridge can collapse in strong winds. The strong wind (driving frequency) across the bridge forced it to sway at its natural frequency. The swaying increased greatly in amplitude, and the structure collapsed. Build dampers into the bridge help lower the amplitudes. Comments for (b) & (c): - While students were able to recall what is meant by resonance, from (b) and (c), it shows that students do not appreciate and understand resonance clearly. - These 2 parts were very poorly attempted. Studen ts answers did not have cla rity and were vague. E.g. simply saying resonance will be reduced. Must clearly state how is it reduced, lower the amplitude. - Many students mix up resonance and damping. - Please note that changing natural frequency is NOT damping.

Meridian Junior College H2 Physics Paper 2 JC2 Preliminary Examinations 2018 3 2 (a)(i) 3 1 1 200 Hz [B1]5.0 10f T Comments: Excellent! (ii) 2 2 2 2 2 1 1 2 2 2 2 Amplitude 5 2 [M1] 25 6.25 [A1]4 Intensity A A A A I I I I I I I Comments: Majority of students did well for this question. A handful of students got the final answer but the presentation was incorrect. Proportionality sign is NOT the same as equal sign. With a proportionality relationship, use ratio method to solve or find the constant k first. (b) (i) The two waves must be coherent, (with constant phase difference between the two waves). [B1] They must either be unpolarised, or polarised in the same plane. [B1] Comments: Generally well done. Common mistakes: Many students wrote the condition where the 2 waves must have similar amplitudes, but this is not accepted as clearly from the question, the amplitudes are not similar. Significant number of students wrote “polarised or unpolarised in the same plane”, this is NOT the same. The polarised wave needs to be in a particular plane but not the unpolarised wave. (ii) If the source is in phase, t heir pa th difference must be eq ual to (n+½) wavelengths where n is an integer. [B1] Or The two waves must meet in antiphase with each other. [B1] Comments: - It is actually crucial to mention that the waves MEET in antiphase , but BOD was given even without the word ‘meet’. - Students need to be aware that antiphase is a very specific term where it is rad out of phase. So by simply writing the waves are out of phase is not good enough.

Meridian Junior College H2 Physics Paper 2 JC2 Preliminary Examinations 2018 4 - For students who wrote the condition of path difference, most answers were incomplete either forgetting t o include the initial condition of the source (in phase or antiphase) or did not specify what ‘n’ refers to. (iii) 2 min 2 2 5For minimum intensity, the resultant amp litude is [M1] 2 5 2 9 2.25 [A1]4 A A A A A I I I I I Comments: Generally well done. Majority of the students know to first find the resultant amplitude before finding the resultant intensity. Again, here students may have the final answer correct but had incorrect presentation. 3 (a) Stationary Wave Progressive Wave Wave profile Varies from one extreme position to another, but does not advance. Advances with the speed of the wave. Energy of wave Energy is retained within the vibratory motion of the wave. Energy is transferred in the direction of wave propagation. Amplitude of oscillation of individual particles Depends on position along the wave Particles at the antinodes oscillate with maximum amplitude Particles at the nodes do not oscillate Same for all particles in the wave regardless of position (assuming no energy loss). Wavelength Twice the distance between 2 adjacent nodes/ antinodes. Equal to the wavelength of the component waves. Distance between any 2 consecutive points on the wave with the same phase. Phase of wave particles in a wavelength All particles bet