Transverse Waves on a Uniform String
For a small-slope transverse disturbance on a uniform flexible string under constant tension T and linear density mu, the propagation speed is sqrt(T/mu), independent of frequency in the ideal nondispersive model.
Why this shows up in the exam
Tension and radius comparisons · Pulse travel times on uniform strings · Sonometer speed calculations
Learn the idea
String-wave speed rises with tension and falls with linear mass density. Tension supplies the transverse restoring force, while mass per unit length supplies inertia, so thick or dense strings carry pulses more slowly at the same tension.
🧠 Memory hook: More pull, more speed; more mass per metre, less speed.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- v = sqrt(T/mu) — transverse-wave speed on an ideal taut string
- mu = rho A — linear density of a uniform wire
- v2/v1 = sqrt((T2 mu1)/(T1 mu2)) — comparison form for two strings
How to approach it
- 1Write mu from the given mass or geometry
- 2Apply sqrt(T/mu) symbolically
- 3Check whether tension is actually uniform
Common slip-ups that cost marks
- •Using total mass instead of linear density without dividing by length
- •Assuming frequency changes at a junction
- •Forgetting area scales as radius squared
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A mass of 1 kg is attached to a spring of force constant 100 N/m. Find the angular frequency of small oscillations.
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