The amplitude of the transverse wave is determined as 0.00118 m.
How to calculate the amplitude of the wave?
The amplitude of the wave is calculated by applying the following formula as shown below;
The angular speed of the wave is calculated as follows;
ω = (a_max) / (v_max)
where;
- a_max is the maximum acceleration
- v_max is the maximum velocity
ω = (8700) / (3.2)
ω = 2,718.75 rad/s
The amplitude of the wave is calculated as follows;
A = (V_max) / ω
A = (3.2 m/s ) / ( 2,718.75 rad/s)
A = 0.00118 m
The complete question is below:
A guitar string is vibrating in its fundamental mode, with nodes at each end. the length of the segment of the string that is free to vibrate is 0.384 m . the maximum transverse acceleration of a point at the middle of the segment is 8700 m/s2 and the maximum transverse velocity is 3.20 m/s . Find the amplitude of the wave.