Waves: Physics 9702 (Cambridge International AS & A Level)

A line of buoys is anchored along a straight channel leading into a harbour. A water wave of frequency $0.40\text{ Hz}$ and wavelength $3.5\text{ m}$ travels along the channel at constant speed, passing each buoy in turn.

(a) State what is meant by the amplitude of a progressive wave. [1]

(b) State what is meant by the wavelength of a progressive wave. [1]

(c) Calculate the speed of the wave. [2]

(d) Calculate the period of the wave. [1]

(e) Two buoys, P and Q, lie along the direction of travel of the wave and are separated by a distance of $0.875\text{ m}$. Determine the phase difference between the oscillations of P and Q, giving your answer in degrees. [2]

An earthquake produces two main types of seismic wave that travel through the Earth: P-waves, which are longitudinal, and S-waves, which are transverse.

(a) By referring to the direction of vibration of particles relative to the direction in which a wave travels, distinguish between a transverse wave and a longitudinal wave. [2]

(b) State one everyday example, other than a seismic wave, of (i) a transverse wave, and (ii) a longitudinal wave. [2]

(c) A seismometer close to the epicentre of an earthquake records an S-wave with an amplitude $2.0$ times greater than the amplitude of an S-wave recorded, at the same instant in its oscillation cycle, by a second seismometer much further away, all other factors being equal. Show that the intensity of the wave at the closer seismometer is $4.0$ times the intensity at the more distant seismometer. [2]

(d) At the more distant seismometer, a later S-wave is recorded with an amplitude $3.0$ times smaller than that of the first S-wave measured there. Calculate the ratio of the intensity of this later wave to the intensity of the first wave, both measured at the same (distant) seismometer. [2]

Four electromagnetic waves, W, X, Y and Z, travel in a vacuum with the following wavelengths.

W: $6.0 \times 10^{-7}\text{ m}$

X: $3.0 \times 10^{-2}\text{ m}$

Y: $1.2 \times 10^{-10}\text{ m}$

Z: $1.5 \times 10^{3}\text{ m}$

Which list places these four waves in order of increasing frequency (lowest frequency first)?

A jet ski travels in a straight line at a constant speed of $20\text{ m s}^{-1}$ along a marked lane on a lake, continuously sounding its horn at a frequency of $600\text{ Hz}$. A lifeguard stands at the end of a wooden jetty that lies directly along the extension of the lane, and listens as the jet ski approaches, passes the jetty, and then continues away in a straight line. The speed of sound in air is $340\text{ m s}^{-1}$.

(a) State the equation for the frequency $f_\text{o}$ heard by a stationary observer when a source of frequency $f_\text{s}$ moves, at speed $v_\text{s}$, directly towards or directly away from the observer, where $v$ is the speed of sound. [1]

(b) Calculate the frequency of the horn heard by the lifeguard while the jet ski is approaching the jetty. [2]

(c) Calculate the frequency of the horn heard by the lifeguard after the jet ski has passed the jetty and is moving away. [2]

(d) Calculate the percentage increase between the frequency found in (b) and the frequency $f_\text{s}$ emitted by the horn. [2]

A student directs plane-polarised light of intensity $I_0$ onto a polarising filter (an analyser) and slowly rotates the analyser. At one particular setting, a light sensor placed behind the analyser measures a transmitted intensity of exactly $0.36I_0$.

According to Malus's law, what is the angle between the analyser's transmission axis and the plane of polarisation of the incident light at this setting?

A loudspeaker emits a sound wave of frequency $250\text{ Hz}$ that travels through still air at a speed of $340\text{ m s}^{-1}$.

(a) State what is meant by the frequency of a progressive wave. [1]

(b) Calculate the wavelength of the sound wave. [2]

(c) Calculate the distance travelled by the wave in a time of $0.050\text{ s}$. [2]

(d) Determine the number of complete wavelengths contained within the distance found in (c). [1]

Which statement correctly describes the difference between a transverse wave and a longitudinal wave?

An ambulance travels in a straight line at constant speed, sounding a siren of frequency $700\text{ Hz}$. A pedestrian stands still, directly in the ambulance's path, and measures the frequency of the sound as $732\text{ Hz}$ while the ambulance approaches. The speed of sound in air is $340\text{ m s}^{-1}$.

(a) Explain, in terms of the wavefronts emitted by the siren, why the pedestrian measures a frequency higher than $700\text{ Hz}$ while the ambulance approaches. [2]

(b) Show that the speed of the ambulance is approximately $14.9\text{ m s}^{-1}$. [3]

(c) Calculate the frequency of the siren heard by the pedestrian just after the ambulance has passed and is moving directly away, assuming its speed is unchanged. [2]

(d) Calculate the wavelength of the sound wave detected by the pedestrian while the ambulance is approaching. [2]

A radio transmitter emits electromagnetic waves of frequency $1.0 \times 10^{8}\text{ Hz}$, which travel through free space at speed $c = 3.00 \times 10^{8}\text{ m s}^{-1}$.

(a) State the region of the electromagnetic spectrum in which this wave lies. [1]

(b) Calculate the wavelength of this wave in free space. [2]

(c) State one property, other than that they are all transverse waves, that is common to every wave in the electromagnetic spectrum. [1]

(d) Explain why electromagnetic waves can be polarised but sound waves cannot. [2]

Unpolarised light of intensity $I_0$ is incident on a first polarising filter, which transmits polarised light of intensity $\tfrac{1}{2}I_0$. This polarised light then passes through a second polarising filter, whose transmission axis is at $60°$ to the transmission axis of the first filter.

What fraction of the original intensity $I_0$ emerges from the second filter?