Verified Solution • 2025–26 Session moderate

Q14.14: NCERT Physics - Part 2 WAVES 14.14 Solution: A wire stretched between two rigid supports vibrates in its…

⚠️ Common Exam Traps & Conceptual Pitfalls

In the fundamental mode the string has a node at each end and an antinode in the middle, so the length equals half a wavelength. Using $lambda=L$ instead of $lambda=2L$ makes the calculated speed half the true value and propagates an error into the tension calculation.

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 _ 10__ kg and its linear mass density is 4.0 _ 10__ kg m__. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string?

Step-by-Step Verified Solution

**Answer:** (a) v=78.75v = 78.75 m/s (b) T=248T = 248 N **Step-by-Step Explanation:** Given: f=45f = 45 Hz, m=3.5×10−2m = 3.5 \times 10^{-2} kg, μ=4.0×10−2\mu = 4.0 \times 10^{-2} kg/m. Length of wire: l=m/μ=0.035/0.04=0.875l = m/\mu = 0.035/0.04 = 0.875 m. For fundamental mode: λ=2l=2×0.875=1.75\lambda = 2l = 2 \times 0.875 = 1.75 m. (a) Speed: v=fλ=45×1.75=78.75v = f\lambda = 45 \times 1.75 = 78.75 m/s. (b) Tension: T=μv2=0.04×(78.75)2=248T = \mu v^2 = 0.04 \times (78.75)^2 = 248 N [citation:2][citation:12].

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

Related Learning Resources & Exam Preparation

Chapter Practice Bank
Practice all topic-wise questions from WAVES
Reference Textbook Solutions
Explore complete chapter exercises for NCERT Physics - Part 2
Competitive PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring