Longitudinal and transverse waves：練習問題

Which of the following waves is correctly classified as a longitudinal wave?

The phenomenon of polarisation provides evidence that light is a transverse wave. What specific characteristic of transverse waves enables them to be polarised?

A beam of initially unpolarised light passes through two ideal polarising filters. The transmission axis of the first filter is vertical. If the second filter is rotated relative to the first until the resulting transmitted light intensity drops to zero, what is the minimum angle through which the second filter must have been rotated?

Which statement correctly describes the relationship between the direction of oscillation of particles/fields and the direction of energy propagation for a transverse wave?

All electromagnetic (EM) waves travel at the same speed in a vacuum. How does the speed of a gamma ray compare to the speed of a radio wave in a vacuum?

What property of particle displacement relative to the direction of energy propagation defines a transverse wave?

A radio wave has a frequency of \(150 \text{ MHz}\) in a vacuum. Given that the speed of all electromagnetic waves in a vacuum is \(3.00 \times 10^8 \text{ m s}^{-1}\), calculate its wavelength.

Explain how the process of polarisation identifies electromagnetic waves as transverse rather than longitudinal, and provide a common application of this property in photography.

A sound wave travels through air at a speed of \(340\, \mathrm{m\, s^{-1}}\) with a frequency of \(680\, \mathrm{Hz}\).

a) Explain the difference between a longitudinal wave and a transverse wave, focusing on the direction of particle oscillation relative to the direction of energy propagation. Give one example of each type of wave. (2 points)

b) Calculate the wavelength of the sound wave in air. (1 point)

c) If this sound wave travels through water at \(1500\, \mathrm{m\, s^{-1}}\) with the same frequency, calculate the percentage increase in wavelength compared to the wave in air. (1 point)

A student investigates the relationship between wave frequency, tension, and the resulting stationary wave patterns on a string of fixed length \(L\) and constant mass per unit length \(\mu\).

a) Write down the equation relating the fundamental frequency \(f\) (first harmonic) to the length \(L\), tension \(T\), and mass per unit length \(\mu\) of the string. (1 point)

b) The student obtains the first harmonic frequency \(f_1 = 120\, \mathrm{Hz}\) when the tension is \(10.0\, \mathrm{N}\). Calculate the required tension if the student wishes to maintain the first harmonic but increase the frequency to \(180\, \mathrm{Hz}\). (2 points)

c) Explain, in terms of wave properties, why only specific frequencies (harmonics) result in the formation of stationary waves on a string fixed at both ends. (2 points)