NUMS — Medical & Dental Entry Test
Take the NUMS Physics — Waves, Sound, Optics and Thermodynamics (Set 7): 30 multiple-choice questions (40 minutes) with instant scoring and a full answer…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. A string of length 0.50 m and mass per unit length 0.010 kg m⁻¹ is fixed at both ends and held under a tension of 100 N. What is the frequency of its fundamental mode?
Answer: C. 100 Hz
Explanation: v = √(T/μ) = √(100/0.010) = 100 m s⁻¹; f₁ = v/2L = 100/1.0 = 100 Hz.
Q2. A pipe 1.00 m long is closed at one end. Taking the speed of sound as 340 m s⁻¹, what is the frequency of the first overtone (the next resonance above the fundamental)?
Answer: D. 255 Hz
Explanation: A closed pipe has only odd harmonics: f₁ = v/4L = 85 Hz, so the first overtone is the third harmonic, 3 × 85 = 255 Hz.
Q3. A source emitting 640 Hz moves towards the observer at 20 m s⁻¹, while the observer moves directly away from the source at 10 m s⁻¹ (speed of sound 340 m s⁻¹). What frequency does the observer hear?
Answer: A. 660 Hz
Explanation: f′ = f₀(v − v_o)/(v − v_s) = 640 × 330/320 = 660 Hz.
Q4. Tuning fork A has a frequency of 440 Hz. Fork B, sounded with it, gives 4 beats per second. When B is loaded with a little wax, the beat frequency falls to 2 per second. What was the frequency of B before loading?
Answer: D. 444 Hz
Explanation: Loading lowers B's frequency. The beats decreased, so B must have been above A: 440 + 4 = 444 Hz, which becomes e.g. 442 Hz (2 beats). If B were 436 Hz, loading would have increased the beats.
Q5. A string of length 1.2 m is fixed at both ends and vibrates in its third harmonic. What is the wavelength of the wave on the string?
Answer: A. 0.80 m
Explanation: For the nth harmonic λ = 2L/n = 2 × 1.2/3 = 0.80 m (there are 3 loops, with 4 nodes including the ends).
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Q6. The speed of sound in air at 0 °C is 332 m s⁻¹. Using v ∝ √T (T in kelvin), what is its speed at 27 °C?
Q7. In Young's double-slit experiment, slits 0.30 mm apart are illuminated with light of wavelength 600 nm and the screen is 1.5 m away. How far from the central bright fringe is the third dark fringe?
Q8. Light of wavelength 500 nm falls normally on a single slit of width 0.20 mm. On a screen 2.0 m away, what is the width of the central bright fringe (between the first minima on either side)?
Q9. A thin soap film (n = 1.33) in air is viewed in reflected light of wavelength 532 nm at normal incidence. What is the smallest non-zero thickness for which the reflected light is brightest?
Q10. Unpolarised light of intensity I₀ passes through two ideal polarising sheets whose transmission axes are at 60° to each other. What intensity emerges?
Q11. A convex mirror has a focal length of magnitude 20 cm. Using the real-is-positive convention (1/u + 1/v = 1/f, with f = −20 cm for a convex mirror), what are the image distance and magnification for an object 20 cm in front of it?
Q12. A converging lens of focal length 25 cm is placed in contact with a diverging lens of power −1.5 D. What is the focal length of the combination?
Q13. A glass slab of thickness 6.0 cm and refractive index 1.5 is placed over a mark on a table. By how much does the mark appear to be raised when viewed from directly above?
Q14. Light travels in glass of refractive index 1.5 towards a glass–water boundary where the refractive index of water is 1.2. What is the critical angle for total internal reflection?
Q15. A thin prism of refracting angle 5.0° is made of glass of refractive index 1.52. What is the approximate deviation of a ray passing through it near normal incidence?
Q16. A window pane of area 1.0 m² and thickness 5.0 mm has its two faces 10 K apart. If the thermal conductivity of glass is 0.80 W m⁻¹ K⁻¹, at what rate does heat flow through the pane?
Q17. A black body radiating at 27 °C is heated to 327 °C. By what factor does the total power radiated per unit area increase?
Q18. A circular hole of diameter 20 mm is drilled in a steel plate (α = 1.2 × 10⁻⁵ K⁻¹). By how much does the diameter of the hole change when the plate is heated by 100 K?
Q19. Two moles of an ideal diatomic gas (Cᵥ = 5R/2, R = 8.314 J mol⁻¹ K⁻¹) are heated at constant pressure through 40 K. What is the increase in internal energy?
Q20. A sample of monatomic ideal gas (γ = 5/3) is compressed adiabatically to half its volume. By what factor does its pressure increase?
Q21. A Carnot engine has a cold reservoir at 300 K. To raise its efficiency to 50% the hot-reservoir temperature must be:
Q22. An ideal (Carnot) refrigerator operates between a freezer at 270 K and a room at 300 K. How much work is needed to remove 900 J of heat from the freezer?
Q23. What is the entropy increase when 0.100 kg of ice melts at 0 °C? (Latent heat of fusion = 3.34 × 10⁵ J kg⁻¹)
Q24. 100 g of ice at 0 °C is added to 400 g of water at 30 °C in an insulated container (latent heat of fusion = 80 cal g⁻¹; specific heat of water = 1.0 cal g⁻¹ °C⁻¹). What is the final temperature?
Q25. At what temperature does the rms speed of oxygen molecules (M = 32) equal that of hydrogen molecules (M = 2) at 27 °C?
Q26. A 0.50 kg mass on a spring of constant 200 N m⁻¹ oscillates with amplitude 5.0 cm. What is its speed when 3.0 cm from the equilibrium position?
Q27. A simple pendulum has a period of 2.00 s on the Earth. What is its period on the Moon, where g is one-sixth of the Earth's value? (Length unchanged)
Q28. A travelling wave is described by y = 0.02 sin(100πt − 5πx), with x and y in metres and t in seconds. What is the speed of the wave?
Q29. A converging lens of focal length 5.0 cm is used as a simple magnifier, with the final image formed at the near point (25 cm from the eye). What is the angular magnification?
Q30. The intensity of sound from a small source at 5.0 m is 8.0 × 10⁻⁶ W m⁻². Assuming the source radiates equally in all directions and nothing is absorbed, what is the intensity at 20 m?