Progressive and stationary waves：練習問題

A sound wave travelling through air is described as a longitudinal wave. Which statement correctly describes the oscillation of the particles in the medium through which this wave travels?

Which statement correctly describes a property of stationary waves on a stretched string?

A stationary wave is formed on a string fixed at both ends with a tension \(T\). The first harmonic frequency is \(f\). If the tension is increased to \(2T\) and the length of the string is doubled while keeping the mass per unit length constant, what is the new first harmonic frequency?

A progressive transverse wave travels along a string. Two points on the string, separated by a distance of \(0.20\text{ m}\), have a phase difference of \(\frac{\pi}{3}\) radians. If the frequency of the wave is \(10\text{ Hz}\), what is the speed of the wave?

In a stationary wave pattern on a string, the distance between the first node and the fourth node is \(60\text{ cm}\). If the speed of the transverse waves on the string is \(150\text{ m s}^{-1}\), what is the frequency of the vibration?

A stationary wave is established on a string of length \(1.20\text{ m}\) fixed at both ends. If the string is vibrating in its third harmonic and the speed of the transverse waves is \(180\text{ m s}^{-1}\), determine the frequency of the vibration.

A progressive wave is described by the equation \(y = A\sin(2\pi(ft - \frac{x}{\lambda}))\). Two points, \(P\) and \(Q\), on the wave are separated by a distance of \(0.15\text{ m}\). If the wavelength is \(0.80\text{ m}\), calculate the phase difference between \(P\) and \(Q\) in radians, giving your answer in terms of \(\pi\).

A uniform wire of length \( 0.75 \text{ m} \) and mass \( 4.5 \text{ g} \) is stretched between two fixed points. The tension in the wire is adjusted to \( 60 \text{ N} \).

(a) Calculate the mass per unit length \( \mu \) of the wire and the speed of a transverse wave on the wire.

(b) Determine the frequency of the first harmonic.

(c) If the tension is increased by 20%, calculate the new frequency of the first harmonic, assuming the length remains constant.