A steel wire is clamped securely at both ends and has a length of 5.6m. It vibrates at its 4th harmonic. It makes 60 complete cycles in 4 seconds. Calculate the wavelength, frequency, period an speed of the wave in the wire. I got f=15Hz, T=0.07s, V= 80m/s lambda=5.3m. Am I right or am I wrong. I'm not sure????

Question

anonymous · Answer

f and T are right. lambda seems wrong, thus speed would be too. Must leave.

anonymous · Answer

How do solve for wavelength?

anonymous · Answer

The first harmonic has half a wavelength, producing nodes (no vibration) at both ends. The second harmonic has two half-wavelengths in that space, thus a wavelength of 5.6m. Third harmonic has 3/2 wavelengths. 4th has 4 x (1/2) lambda = 2 wavelengths in 5.6m, so one wavelength is 5.6/2 = 2.8 m.

anonymous · Answer

Speed would be frequency times that wavelength.