Nature and Properties of Waves：練習問題

A longitudinal wave travels through a long helical spring. At a certain instant, the distance between the center of a compression and the center of the next adjacent rarefaction is measured to be \(0.15 \text{ m}\). If the frequency of the vibration is \(20 \text{ Hz}\), what is the speed of the wave?

A progressive wave is travelling along a stretched string. At a certain instant, the displacement-distance graph shows a wavelength of \(0.80 \text{ m}\). A particle on the string takes \(0.10 \text{ s}\) to move from its equilibrium position to its maximum positive displacement for the first time. What is the speed of this wave?

A uniform string is stretched between two fixed supports. When the tension in the string is \(T\), the fundamental frequency of vibration is \(f_0\). If the tension is increased to \(1.44T\) and the length of the string is reduced by \(10\%\), what is the new fundamental frequency?

Which of the following properties of a progressive mechanical wave is not determined by the source of the wave alone, but also depends on the properties of the medium through which it travels?

A stationary wave is formed on a string of length \(L\) fixed at both ends. When the string vibrates in its third harmonic, which of the following statements is incorrect?

A mechanical wave propagates along a uniform horizontal spring. At a specific instant, the distance between the center of a compression and the center of the third subsequent compression is measured to be \(0.45 \text{ m}\). If the wave generator oscillates at a frequency of \(15 \text{ Hz}\), calculate the speed of the wave.

In a Young's double-slit experiment, the fringe separation on a screen is \(w\). If the monochromatic light source is replaced by one with a frequency \(1.2\) times the original frequency, and the distance from the slits to the screen is simultaneously doubled, calculate the new fringe separation in terms of \(w\).

A point source in a ripple tank produces circular waves of wavelength \(\lambda\). Two points, \(X\) and \(Y\), are located at distances of \(4.2\lambda\) and \(5.7\lambda\) from the source respectively. Determine the phase difference between the oscillations at \(X\) and \(Y\) in radians.

A sound wave in air has a frequency of \(500 \text{ Hz}\) and a wavelength of \(0.68 \text{ m}\).

(a) (i) Calculate the speed of this sound wave in air.

(a) (ii) State whether a sound wave is a transverse wave or a longitudinal wave.

(b) Explain briefly how energy is transferred by a wave.

(a) Define the term diffraction.

(b) Describe how the phenomenon of diffraction can be demonstrated using water waves in a ripple tank, specifically mentioning a suitable experimental setup.

(c) Explain how the degree of diffraction is affected by:

(i) the width of the gap the waves pass through.

(ii) the wavelength of the waves.