Physics chapter 16 #1 h/w

Question

A guitar string with a linear density of 2.0 g/m is stretched between supports that are 60 cm apart. The string is observed to form a standing wave with three anti-nodes when driven at a frequency of 420 Hz.

1) What is the frequency of the fifth harmonic of this string?

2) What is the tension in the string?

Answer 1

three anti-nodes means the third harmonic, so the fundamental is 420/3 = 140 Hz.

The fifth harmonic = 5*140 = 720 Hz

The wavelength of the fundamental is double to length of the string

wave velocity = wavelength * frequency = 1.2 * 140 = 168 m/s

tension = velocity^2 * density = (168)^2 * 0.002 = 56.5 newtons