Question

A 4.0 g string, 0.36 m long, is under tension. The string produces a 500 Hz tone when it vibrates in the third harmonic. The speed of sound in air is 344 m/s. In this situation, the wavelength of the standing wave in the string, in SI units, is closest to:

Answer 1

Answer:

$\lambda = 0.24 m$

Explanation:

The string vibrates in the third harmonics, n = 3

Length of the string, l = 0.36 m

Frequency of the tone produced, f = 500 Hz

The speed of sound in air is 344 m/s

Calculate the speed of sound produced by the string in the third harmonics:

The frequency of sound is given by the formula:

$f = \frac{nv}{2l} \\500 = \frac{3v}{2*0.36}\\500 * 2 * 0.36 = 3v\\v = 360/3\\v = 120 m/s\\v = \lambda f\\\lambda = v/f\\\lambda = 120/500\\\lambda = 0.24 m$