Final answer:
The speed of propagation of transverse waves in the wire is 26.24 m/s.
The tension in the wire is 0.3724 N.
The magnitude of the maximum transverse velocity of particles in the wire is 1.149 m/s.
Step-by-step explanation:
=> To calculate the speed of propagation of transverse waves in the wire, we need to use the formula:
speed = frequency * wavelength
Given that the frequency is 64.0 Hz and the distance between the ends of the wire is 82.0 cm, we can calculate the wavelength:
wavelength = distance between ends / number of antinodes = 82.0 cm / 2 = 41.0 cm
= 0.41 m
Therefore, the speed of propagation of transverse waves in the wire is:
speed = 64.0 Hz * 0.41 m
= 26.24 m/s
=> To find the tension in the wire, we can use the formula:
tension = mass * gravity
Given that the mass of the wire is 38.0 g = 0.038 kg and the gravitational acceleration is 9.8 m/s², we can calculate the tension:
tension = 0.038 kg * 9.8 m/s²
= 0.3724 N
Therefore, the tension in the wire is: tension = 0.3724 N
=> To find the magnitude of the maximum transverse velocity of particles in the wire, we can use the formula:
velocity = amplitude * angular frequency
Given that the amplitude at the antinodes is 0.290 cm = 0.0029 m and the angular frequency is given by the equation w = 2 * pi * f, where f is the frequency, we can calculate the maximum transverse velocity:
angular frequency = 2 * pi * 64.0 Hz
= 128 * pi rad/s
velocity = 0.0029 m * 128 * pi rad/s
= 0.366 m/s * pi rad/s
= 1.149 m/s
Therefore, the magnitude of the maximum transverse velocity of particles in the wire is: velocity = 1.149 m/s