1. ans: 1.73; use v = sqrt(T/m).

3. ans: 0 or 2p; the waves are in step, so crests are on crests, etc.

4. ans: 40 Hz; use f = v/l.

5. ans: 328 m/s; use v = f*l.

6. ans: 0.58; use v = sqrt(T/m).

9. ans: 0; hard reflection reverses the pulse, which momentarily cancels the displacement (but not the velocity, so the wave continues).

10. ans: 5.5 mm; use l = v/f. Don't forget the "k" in kHz, and the mm conversion.

11. ans: 260 m/s; use v = sqrt(T/m). Don't forget to convert everything to SI units.

12. ans: 3 Hz; beat frequency = difference of two nearly equal frequencies.