Wave Speed in Elastic Media
For small disturbances in a homogeneous elastic medium, wave speed is the square root of the appropriate elastic modulus divided by mass density, with the modulus chosen for the actual deformation mode.
Why this shows up in the exam
Sound-speed comparisons across materials · Temperature and gas-composition scaling · Percentage-change calculations for modulus and density
Learn the idea
Mechanical-wave speed is set by the medium's restoring stiffness divided by its inertia. A stiffer medium restores a disturbance faster, while greater density makes the same disturbance harder to accelerate; geometry selects the relevant elastic modulus.
🧠 Memory hook: Stiffness speeds; density slows.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- v_longitudinal = sqrt(Y/rho) — longitudinal speed in a slender solid rod
- v_sound = sqrt(B/rho) — compressional-wave speed in a fluid
- v_gas = sqrt(gamma R T/M) — ideal-gas sound speed at absolute temperature T
How to approach it
- 1Identify the deformation and correct modulus
- 2Form a ratio before inserting values
- 3Check dimensions and the direction of change
Common slip-ups that cost marks
- •Using Celsius instead of kelvin in square-root scaling
- •Using Young's modulus for a fluid
- •Assuming sound speed follows source speed
🌟 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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