Read Vertical Strings: Let Tension Vary with Height
Pulse speed on a string is square-root(T/λ), but a hanging string has tension that changes with distance from the support.
Transverse Pulses on a Vertical String is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
Start with the condition
At depth x from the top, tension supports the string below that point.
Build the governing relation
Use the mass of the hanging portion, not the full string, when writing local tension.
Finish with a physical check
Check the limiting case before selecting an option: remove the special feature in the diagram or make the relevant parameter very large or very small. The result should reduce to a familiar relation.
OlympIQ exam lens
- ✓State the physical condition before choosing a formula.
- ✓Keep direction, sign and constraint information explicit.
- ✓Test one limiting case before committing to an option.
Applying one constant wave speed to the entire vertical string ignores its varying tension.
Ready to try the pattern?
100% coverage across the linked question.
Practise the linked question