Resonance (amplification at natural frequency) is exploited in musical instruments (e.g., guitar body resonates with string frequencies) and tuning forks (designed to vibrate at precise frequency for calibration). Memory tip: 'Resonance applications: musical instruments (amplify sound), tuning forks (frequency standard), bridges (avoid resonance to prevent collapse)'. This application question tests wave phenomena uses, frequently appearing in competitive exams. Always link physical principles to practical applications; competitive exams emphasize real-world relevance of physics concepts, including both beneficial and hazardous aspects of resonance.
Explanation:
Resistance R = rhoL/A. If the wire is stretched so length becomes L' = 2L, the volume (V = AL) must remain constant. Therefore, the new area A' must be A/2 to maintain V. The new resistance R' = rho(2L)/(A/2) = 4 * (rhoL/A) = 4R. Stretching a wire to double its length increases its resistance strictly by a factor of 4. This is a classic trap question compared to merely 'changing the wire'.
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