Frequency of sound wave determines: MCQ with Answer and Explanation
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Question #1
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Two slabs of equal thickness and cross-sectional area have thermal conductivities K1 and K2. If they are joined in series, the equivalent thermal conductivity of the combination is:
Correct Answer: Option C
Explanation:
For slabs in series, the rate of heat flow (H) is the same. Total resistance R_eq = R1 + R2. Since thermal resistance R = L / (KA), and total length is 2L: (2L) / (K_eq * A) = (L / K1A) + (L / K2A). Canceling L/A yields 2/K_eq = 1/K1 + 1/K2. Solving gives K_eq = 2K1K2 / (K1 + K2).
For slabs in series, the rate of heat flow (H) is the same. Total resistance R_eq = R1 + R2. Since thermal resistance R = L / (KA), and total length is 2L: (2L) / (K_eq * A) = (L / K1A) + (L / K2A). Canceling L/A yields 2/K_eq = 1/K1 + 1/K2. Solving gives K_eq = 2K1K2 / (K1 + K2).
Question #2
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When a wave travels from one medium to another, which of its properties never changes?
Correct Answer: Option B
Explanation:
When a wave (like light or sound) changes mediums, its velocity changes due to the new medium's optical or mechanical density. Wavelength changes proportionally with velocity (v = fλ). However, frequency is determined solely by the source generating the wave and the energy of the photons/particles, and it remains absolutely constant.
When a wave (like light or sound) changes mediums, its velocity changes due to the new medium's optical or mechanical density. Wavelength changes proportionally with velocity (v = fλ). However, frequency is determined solely by the source generating the wave and the energy of the photons/particles, and it remains absolutely constant.
Question #3
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The magnetic field at the center of a circular coil of radius R carrying current I is:
Correct Answer: Option C
Explanation:
For a circular coil with N turns, magnetic field at center B = μ₀NI/(2R). For single turn (N=1), B = μ₀I/(2R). This derives from Biot-Savart law. Option A is for single turn; B and D have incorrect constants. Memory tip: 'Coil center: B = μ₀NI/(2R); straight wire: B = μ₀I/(2πr)'. This formula application is frequently tested in magnetism sections of competitive exams. Always note number of turns N; competitive exams often include it to test attention to detail.
For a circular coil with N turns, magnetic field at center B = μ₀NI/(2R). For single turn (N=1), B = μ₀I/(2R). This derives from Biot-Savart law. Option A is for single turn; B and D have incorrect constants. Memory tip: 'Coil center: B = μ₀NI/(2R); straight wire: B = μ₀I/(2πr)'. This formula application is frequently tested in magnetism sections of competitive exams. Always note number of turns N; competitive exams often include it to test attention to detail.
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