Waves：練習問題

A progressive sound wave has a frequency of \( 440 \text{ Hz} \) and travels through air at a speed of \( 330 \text{ m s}^{-1} \). What is the phase difference between two points on the wave that are separated by a distance of \( 0.25 \text{ m} \)?

Unpolarised light of intensity \( I_0 \) is incident on a linear polariser. The light then passes through a second polariser whose transmission axis is at an angle of \( 60^\circ \) to the first. What is the intensity of the light emerging from the second polariser?

A point source of sound emits energy uniformly in all directions. At a distance \( r \) from the source, the amplitude of the sound wave is \( A \). The power output of the source is then doubled, and the distance from the source is increased to \( 2r \). What is the new amplitude of the sound wave at this new distance?

Which statement about electromagnetic waves is correct?

A cathode-ray oscilloscope (CRO) displays a trace of a sound wave. The time-base is set to \( 5.0\text{ ms cm}^{-1} \). A student observes that two complete cycles of the wave occupy a horizontal distance of \( 8.0\text{ cm} \) on the screen. What is the frequency of the sound wave?

The intensity of a wave is \( I \) when its amplitude is \( A \). If the amplitude is increased to \( 3A \), calculate the new intensity in terms of \( I \).

A car horn emits a sound of frequency \( 400\text{ Hz} \) as it approaches a stationary observer at a speed of \( 25\text{ m s}^{-1} \). If the speed of sound is \( 330\text{ m s}^{-1} \), calculate the frequency heard by the observer.

Unpolarized light of intensity \( I_0 \) is incident on a polarizer. The transmitted light then passes through a second polarizer (analyzer). If the transmission axis of the analyzer is at an angle \( \theta \) to the first polarizer, and the final transmitted intensity is \( 0.125I_0 \), determine the value of \( \theta \).

A progressive wave travels through a medium. The wave is described by its frequency, wavelength, and amplitude.

(a) Define the frequency of a progressive wave.
(b) A sound wave has a frequency of \( 440 \text{ Hz} \) and travels at a speed of \( 330 \text{ m s}^{-1} \). Calculate the wavelength of this sound wave.
(c) The intensity of a second sound wave is four times the intensity of the first wave. If the first wave has an amplitude \( A \), determine the amplitude of the second wave in terms of \( A \), assuming both waves have the same frequency.

A car travels at a constant speed of \( 25 \text{ m s}^{-1} \) towards a stationary observer while sounding its horn. The horn emits a sound wave of frequency \( 800 \text{ Hz} \). The speed of sound in air is \( 340 \text{ m s}^{-1} \).

(a) Calculate the frequency of the sound heard by the stationary observer as the car approaches.
(b) After passing the observer, the car continues at the same speed away from the observer. Calculate the change in the frequency heard by the observer as the car passes them.
(c) The observer now begins to move in the same direction as the car at a speed of \( 10 \text{ m s}^{-1} \) while the car is moving away. Qualitatively describe what happens to the observed frequency compared to part (b).