A string with both ends held fixed is vibrating in its third harmonic. The waves have a speed of 186 m/s and a frequency of 205 Hz. The amplitude of the standing wave at an antinode is 0.440 cm.

Calculate the amplitude at a point on the string a distance of 20.0 cm from the left-hand end of the string.

Calculate the maximum transverse velocity of the string at this point.

The maximum transverse velocity of the string at an antinode can be calculated using the formula 2 \\pi \\cdot frequency \\cdot amplitude, resulting in approximately 5.68 m/s.

Explanation:

The question asks how to calculate the maximum transverse velocity of a string vibrating in its third harmonic when the amplitude at an antinode is given.

The wave speed and frequency are also provided. The maximum transverse velocity at an antinode in a standing wave can be obtained using the formula:

velocity (v) = 2 \\pi \\cdot frequency (f) \\cdot amplitude (A)

Given that the frequency is 205 Hz and the amplitude is 0.440 cm (or 0.0044 meters), we can calculate the velocity as follows:

v = 2 \\pi \\cdot 205 Hz \\cdot 0.0044 m

v = approximately 5.68 m/s