High School

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.

Answer :

Final answer:

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

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