A wave has frequency 50 Hz and wavelength 2 m. Its speed is:
A. 50 m/s
B. 100 m/s
C. 200 m/s
D. 25 m/s
Answer: Option B
Solution (By JKExamLibrary)
Wave speed v = frequency (f) × wavelength (λ). Thus v = 50 Hz × 2 m = 100 m/s. This fundamental wave equation applies to all periodic waves (sound, light, water). Memory aid: 'v = fλ – the universal wave equation'. Competitive exams frequently test this direct calculation. Always ensure units: Hz = s⁻¹, so (s⁻¹)×m = m/s, correct for speed. This problem assesses basic wave property understanding, crucial for sound and light topics.
Explanation:
Diffraction (bending of waves around obstacles) is a characteristic wave phenomenon, explained by Huygens' principle and wave superposition. It demonstrates light's wave nature, as particles would travel in straight lines. Particle nature is shown by photoelectric effect; dual nature combines both. Memory aid: 'Diffraction/interference ⇒ wave nature; photoelectric effect ⇒ particle nature'. This conceptual question tests wave-particle duality fundamentals, frequently examined in competitive exams. Always link specific phenomena to the aspect of light they demonstrate; competitive exams often combine both aspects in advanced questions requiring nuanced understanding.
Explanation:
Escape velocity v_e = √(2GM/R), where M is planet mass, R its radius. Thus v_e depends on both M and R. It is independent of the escaping body's mass (as gravitational and inertial mass cancel). Memory tip: 'v_e ∝ √(M/R); larger M or smaller R ⇒ higher escape velocity'. This gravitation formula application is frequently tested in competitive exams. Always recall that escape velocity is a property of the planet, not the projectile. This problem assesses understanding of gravitational potential energy concepts.
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