Oscillations & Waves — Physics

Q.1

WBCS Prelims 2021

A person on a swing stands up. The time period of the swing

A. increases

B. remains the same

C. decreases

D. becomes zero

Explanation

Core Formula/Logic: Time period of a simple pendulum T = 2π√(L/g), where L is effective length from pivot to center of mass.
Step-by-Step Solution: 1. When standing up, the person's center of mass rises upward relative to the swing seat. 2. This reduces effective length L from pivot point to center of mass. 3. Since T ∝ √L, decreasing L decreases T.
Common Pitfall: Assuming swing rope length is only factor gives option B. Thinking standing increases length produces option A. Option D is physically impossible as time period cannot be zero.
Shortcut/Takeaway: For any pendulum: shorter length = shorter period. Standing up reduces effective length, so period decreases.

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Q.2

WBCS Prelims 2021

The waves produced by motor boat sailing on water are

A. transverse

B. longitudinal

C. longitudinal and transverse

D. stationary

Explanation

Why Correct: A motor boat generates both transverse surface waves (water ripples with particle motion perpendicular to wave direction) and longitudinal pressure waves (sound waves in water with particle motion parallel to wave direction) as it moves through the fluid.
Distractor Analysis: Transverse waves alone describe only the surface water waves. Longitudinal waves alone describe only the sound waves in water. Stationary waves require interference between two identical waves traveling in opposite directions, which a single moving boat does not create.
Takeaway: Many moving objects in fluids produce both transverse surface waves and longitudinal pressure waves simultaneously, with water waves being transverse and sound waves in water being longitudinal.

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Q.3

WBCS Prelims 2016

X-rays are

A. electromagnetic radiations of very short wavelength

B. beams of electrons

C. electromagnetic radiations of very long wavelength

D. visible to the naked eye

Explanation

Why Correct: X-rays are electromagnetic waves with wavelengths between 0.01 to 10 nanometers, shorter than ultraviolet but longer than gamma rays.
Distractor Analysis: Electron beams constitute cathode rays, not X-rays. Very long wavelength electromagnetic radiation describes radio waves. Human eyes detect wavelengths from 400-700 nm (visible light), while X-rays require photographic plates or detectors.
Takeaway: The electromagnetic spectrum orders radiation by wavelength: radio waves (longest) > microwaves > infrared > visible light > ultraviolet > X-rays > gamma rays (shortest).

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Q.4

WBCS Prelims 2011

A spring has length l and spring constant K. It is cut into two pieces of lengths l1 and l2 . If l1 = nl2 , the spring constant of the spring of length l1 is

A. K(l + n) / n

B. K(l + n)

C. Kn / (l + n)

D. K / (l + n)

Explanation

Why Correct: The spring constant of a cut piece is inversely proportional to its length relative to the original spring. For piece l1 = n*l2, the original constant K scales by total length over piece length: k1 = K*l/l1 = K*(n+1)/n.
Distractor Analysis: K(l+n)/n incorrectly adds length and dimensionless n. K(l+n) omits the necessary division by n and ignores inverse proportionality. K/(l+n) has units of constant per length, which is not a spring constant.
Takeaway: When a spring of constant K and length L is cut into pieces, the new constant for a piece of length l is K*L/l.

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Q.5

WBCS Prelims 2008

Which one of the following is not an electromagnetic wave?

A. Radio wave

B. X-ray

C. Visible light

D. Sound wave

Explanation

Why Correct: Sound waves are mechanical waves that require a medium to propagate, while electromagnetic waves can travel through vacuum.
Distractor Analysis: Radio waves, X-rays, and visible light are all electromagnetic waves with different wavelengths and frequencies in the electromagnetic spectrum.
Takeaway: Electromagnetic waves include radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays—all travel at the speed of light in vacuum (3×10^8 m/s).

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Q.6

WBCS Prelims 2006

The nature of motion of a sewing machine is

A. Circular motion

B. Translational motion

C. Oscillatory motion

D. Rotational motion

Explanation

Why Correct: A sewing machine's needle moves in oscillatory motion—it repeatedly moves back-and-forth about a fixed mean position, which defines oscillation.
Distractor Analysis: Circular motion requires following a circular path, which the needle does not do. Translational motion involves straight-line movement without returning to a starting point. Rotational motion involves spinning about an axis, while the needle translates while oscillating.
Takeaway: Other oscillatory motion examples include pendulum swings, vibrating strings, and piston movement in engines—all feature periodic to-and-fro motion about equilibrium.

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Q.7

WBCS Prelims 2005

X-ray fails to pass through

A. Flesh

B. Bone

C. Iron

D. Gold

Explanation

Why Correct: Gold has a high atomic number (79) and electron density, making it highly effective at absorbing X-rays due to strong photoelectric absorption.
Distractor Analysis: Flesh consists mostly of low-Z elements like hydrogen, carbon, and oxygen, allowing X-rays to pass through easily. Bone contains calcium and phosphorus, which absorb some X-rays but less than heavy metals. Iron (atomic number 26) absorbs X-rays moderately but less effectively than gold.
Takeaway: In medical imaging, lead (atomic number 82) is used for radiation shielding because it absorbs X-rays even more effectively than gold.

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