Question

A string that is fixed at both ends has a length of 2.50 m. When the string vibrates at a frequency of 85.0 Hz, a standing wave with five loops is formed.

1. What is the speed of the waves?

Answer 1

Five loops means that there are four nodes inside the string, and that n is 5. The wavelength is (2L)/n = 2(2.50 m)/5 = 1.00 m. Alternatively, you can recognize that five loops is two and a half waves, and (2.50 m)/(2.5) = 1.00 m.

What is the speed of the waves?

v = fl = (85.0 Hz)(1.00 m) = 85.0 m/s

Answer 2

In general, for any wave,

v = f?, speed = frequency times wavelength. We know the frequency and the wavelength, f = 85.0 Hz, ? = 1.0 m, so v = (85.0 Hz)(1.0 m) = 85.0 m/s