The Doppler effect refers to the change in frequency of a wave in relation to an observer moving relative to the wave source.

The phenomenon of two sound waves of slightly different frequencies interfering is called beats.

Damping causes the amplitude of oscillations to decrease over time due to energy loss.

Damping causes the energy of the oscillating system to decrease over time due to energy loss.

Increasing temperature increases the speed of sound in air.

Increasing tension in the string increases the speed of the wave.

Increasing the amplitude of a sound wave increases its loudness.

Increasing the amplitude of a wave increases its energy, as energy is proportional to the square of the amplitude.

Increasing the damping coefficient decreases the amplitude of oscillation in a damped oscillator.

Increasing the tension in a string increases the speed of the wave, as speed is proportional to the square root of tension.

Increasing the tension in a string increases the speed of the wave traveling through it, as speed is proportional to the square root of tension.

The speed of sound in air increases with an increase in temperature.

The displacement of a damped harmonic oscillator is given by x(t) = A e^(-bt) cos(ωt), where b is the damping coefficient.

The equation of motion for a damped harmonic oscillator is m d²x/dt² + b dx/dt + kx = 0.

The equation of motion for SHM is x(t) = A cos(ωt) or x(t) = A sin(ωt).

Frequency (f) = speed/wavelength = 343 m/s / 0.5 m = 686 Hz.

Frequency (f) = Speed (v) / Wavelength (λ) = 340 m/s / 0.5 m = 680 Hz.

Frequency f is the reciprocal of the period T, given by f = 1/T. Therefore, f = 1/0.02 s = 50 Hz.

Frequency f is the reciprocal of the period T. Therefore, f = 1/T = 1/0.01 s = 100 Hz.

The fundamental frequency is given by f = v/λ. For a pipe open at both ends, λ = 2L = 4 m. Thus, f = 343 m/s / 4 m = 85.75 Hz, approximately 85 Hz.

The fundamental frequency is given by f = v/λ; for a pipe open at both ends, λ = 2L, so f = v/(2L) = 343/(2*2) = 42.875 Hz.

The equation x(t) = A e^(-bt) cos(ωt) describes the motion of a damped harmonic oscillator.

The equation of motion for a damped harmonic oscillator includes a damping term and is given by m d²x/dt² + b dx/dt + kx = 0.

The equation of motion for a damped oscillator includes a damping term (b dx/dt) along with the restoring force (kx).

The period T of a simple pendulum is given by T = 2π√(L/g). For L = 1 m and g ≈ 9.8 m/s², T = 2π√(1/9.8) ≈ 2 s.

In simple harmonic motion, acceleration is always opposite to displacement, hence the phase difference is 180 degrees.

In simple harmonic motion, the acceleration is always directed towards the mean position and is 180 degrees out of phase with the displacement.

In simple harmonic motion, acceleration is 180 degrees out of phase with displacement.

At resonance, the phase difference is 90°.

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