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Q14.3: NCERT Physics - Part 2 WAVES 14.3 Solution: A steel wire has a length of 12.0 m and a mass of 2.10 kg. What …

⚠️ Common Exam Traps & Conceptual Pitfalls

When using $v=sqrt{T/mu}$ for a string, solve for $T$ by squaring the velocity first and then multiplying by the linear density: $T=v^2,mu$. Students often mistakenly square the product $vmu$ or forget the square root, leading to a tension value that is off by a factor of $mu$ or its square. Carefully isolate $T$ before squaring to avoid this error.

A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at 20 �C = 343 m s__

Step-by-Step Verified Solution

**Answer:** T=2.06×104 NT = 2.06 \times 10^4 \text{ N} **Step-by-Step Explanation:** Given: l=12.0l = 12.0 m, m=2.10m = 2.10 kg, v=343v = 343 m/s. Linear mass density:
μ=ml=2.1012=0.175 kg/m\mu = \frac{m}{l} = \frac{2.10}{12} = 0.175 \text{ kg/m}
Using v=T/μv = \sqrt{T/\mu}:
T=v2μ=(343)2×0.175=20588.6 N≈2.06×104 NT = v^2 \mu = (343)^2 \times 0.175 = 20588.6 \text{ N} \approx 2.06 \times 10^4 \text{ N}
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All Questions in this Chapter

Q14.1 Q14.2 Q14.3 Q14.4 Q14.5 Q14.6 Q14.7 Q14.8 Q14.9 Q14.10 Q14.11 Q14.12 Q14.13 Q14.14 Q14.15 Q14.16 Q14.17 Q14.18 Q14.19

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