At resonance, the phase difference between the driving force and the displacement is 0 degrees.

If two particles are in the same position at the same time in simple harmonic motion, they have a phase difference of 0.

A phase difference of 90 degrees corresponds to π/2 radians.

When two particles are in phase, they reach their maximum and minimum displacements at the same time, resulting in a phase difference of 0 radians.

The phase difference between two points in the same wave separated by a distance of λ/2 is π radians.

The phase difference Δφ between two points separated by a distance of λ/4 is given by Δφ = (2π/λ)(λ/4) = π/2 radians.

The phase difference between two points that are half a wavelength apart is π radians.

The phase difference between two points on a wave that are one wavelength apart is 2π radians.

The bending of sound waves around obstacles is known as diffraction.

The potential energy (PE) stored in a spring is given by PE = 1/2 kx², where k is the spring constant and x is the displacement.

Sonar technology is based on the reflection of sound waves to detect objects underwater.

The Doppler effect is the change in frequency (and wavelength) of a wave in relation to an observer moving relative to the wave source.

Sonar works on the principle of reflection of sound waves to detect objects underwater.

The principle of superposition states that when two or more waves overlap, the resultant displacement is the sum of the individual displacements.

The typical range of human hearing is from 20 Hz to 20 kHz.

The typical range of human hearing is from 20 Hz to 20 kHz.

Frequency and wavelength are inversely proportional when the speed of the wave is constant, as given by the equation v = fλ.

The amplitude of a damped oscillator decreases exponentially with time.

Critical damping occurs at a specific value of the damping coefficient, which separates under-damping from over-damping.

A damping ratio of 1 indicates critical damping, while less than 1 indicates underdamping and greater than 1 indicates overdamping.

A damping ratio less than 1 indicates underdamping, equal to 1 indicates critical damping, and greater than 1 indicates overdamping.

The relationship is given by Frequency = 1/Period.

The frequency (f) is the reciprocal of the period (T), so f = 1/T.

The period (T) is the reciprocal of frequency (f), so T = 1/f.

The period T of a mass-spring system is given by T = 2π√(m/k).

At maximum displacement, all energy is potential energy (PE), and kinetic energy (KE) is zero.

The speed v of a wave on a string is given by v = √(T/μ), where T is the tension and μ is the mass per unit length. Here, v = √(100/0.5) = √200 = 10 m/s.

The speed of a wave on a string is given by the formula v = sqrt(T/μ), where T is the tension and μ is the mass per unit length. Here, v = sqrt(100/2) = sqrt(50) = 10 m/s.

The speed of sound in air at 20°C is approximately 343 m/s.

The speed of sound in air at 20°C is approximately 343 m/s.