A student stands $85\ \text{m}$ from a large flat wall and makes a short loud sound. The time between making the sound and hearing the echo is $0.50\ \text{s}$.

Ultraviolet radiation in a vacuum has a wavelength of $2.5\times10^{-7}\ \text{m}$. The speed of electromagnetic waves in a vacuum is $3.00\times10^8\ \text{m s}^{-1}$.

A transverse wave travels along a stretched string from left to right. The graph shows the displacement $y$ of points on the string against distance $x$ at one instant. Point P is marked on the graph.

The table gives approximate wavelength ranges for some regions of the electromagnetic spectrum. A visible green laser has wavelength $5.4\times 10^{-7}\ \text{m}$ in air.

A small lamp emits electromagnetic radiation uniformly in all directions with a power of $60\ \text{W}$. Absorption by air is negligible.

A transverse wave on a string travels from left to right. The graph shows the displacement of the string against position at one instant. Points P and Q mark two particles of the string.

An ultrasound probe emits a short pulse of frequency $2.0\ \text{MHz}$ for a time of $8.0\times10^{-6}\ \text{s}$. The speed of ultrasound in soft tissue is $1540\ \text{m s}^{-1}$.

Monochromatic visible light of frequency $5.0\times10^{14}\ \text{Hz}$ travels from air into a transparent material. Its speed in air is $3.00\times10^8\ \text{m s}^{-1}$ and its speed in the material is $2.00\times10^8\ \text{m s}^{-1}$.

A rescue team uses both radio communication and ultrasound imaging during an emergency response.

A student measures the speed of sound in air using a loudspeaker connected to a signal generator and two microphones connected to an oscilloscope. The frequency of the sound is $2.50\ \text{kHz}$. One microphone is fixed. The table shows positions of the second microphone for which the two oscilloscope traces are in phase.

A longitudinal wave travels to the right along a spring. The graph shows the displacement $s$ of coils from their equilibrium positions against distance $x$ along the spring at one instant. Positive displacement is to the right. Points A, B and C are marked on the graph.

A small lamp radiates uniformly in all directions. The graph shows how the measured intensity $I$ of the light depends on distance $r$ from the lamp. Absorption by air is negligible.

Three wave signals are tested in different situations. The table summarizes the source, the region between source and detector, and whether a signal is detected.

The graph shows particle displacement against position for a longitudinal sound wave travelling to the right in air. Three positions A, B and C are labelled.

Two smartphones are used as microphones to measure the speed of sound. The phones are placed $0.50\ \text{m}$ apart along the path of a sharp sound. The sampling rate of each phone is $44.1\ \text{kHz}$. Take the speed of sound to be $340\ \text{m s}^{-1}$.

A wave source produces a short train of transverse waves on the surface of water. The oscilloscope trace shows the displacement of the source against time. A photograph shows the wave train on the water at a later instant.

A transverse wave travels to the right along a string. The visual shows a displacement-distance graph at $t=0$ and a displacement-time graph for point A on the string. Point B is also marked on the displacement-distance graph.

A loudspeaker produces a steady sound wave in air. The table shows, at one instant, how particle displacement and pressure variation depend on distance from the loudspeaker. Points P, Q and R are marked.

A monochromatic beam of light from a laser travels from air into glass. The table gives the frequency of the laser light and the speed of light in each medium.

A ripple tank is used to study water waves travelling from a deeper region into a shallower region. The wave source oscillates at a constant frequency. The visual shows the displacement-time graph of the source and snapshots of wavefront spacing in the two regions.

A transverse wave travels to the right along a taut horizontal rope. The source vibrates with a frequency of $5.0\ \text{Hz}$. Adjacent crests on the rope are separated by $0.80\ \text{m}$. Point $P$ is instantaneously at its equilibrium position on a part of the wave where the displacement decreases with distance to the right.

A student measures the speed of sound in air using two microphones connected to an oscilloscope. A loudspeaker emits a continuous sound of frequency $2.50\ \text{kHz}$. One microphone is fixed. The second microphone is moved along a straight line away from the loudspeaker. The distance between the first and fifth positions where the two traces are in phase is $0.548\ \text{m}$.

A wave source on the surface of water emits $12$ complete cycles at a frequency of $40\ \text{Hz}$ and then stops. The wave speed in deep water is $1.6\ \text{m s}^{-1}$. The wave train later enters shallow water where its speed is $1.2\ \text{m s}^{-1}$.

A detector measures the intensity of microwave radiation from a small transmitter at different distances. The graph shows $I$ plotted against $1/r^2$, where $r$ is the distance from the transmitter. The transmitter is intended to radiate uniformly in all directions.

A radio transmitter radiates electromagnetic waves uniformly in all directions with a power of $60\ \text{W}$. A receiver is at a distance of $2.5\ \text{km}$ from the transmitter. Assume there is no absorption.

A longitudinal sound wave travels to the right in a tube. The graph shows the displacement $s$ of air molecules from their equilibrium positions against position $x$ along the tube at one instant. Positive displacement is to the right. Points A and B are both at zero displacement. At A the displacement graph has a negative gradient; at B it has a positive gradient. The distance from A to the next point with the same state of oscillation is $0.68\ \text{m}$. The speed of sound in the tube is $340\ \text{m s}^{-1}$.

A student estimates the speed of sound using echoes from a large flat wall. The student stands $85.0\ \text{m}$ from the wall and measures a time interval of $0.50\ \text{s}$ between making a sharp sound and hearing the echo. The uncertainty in the time measurement is estimated as $\pm0.05\ \text{s}$.

Light from a distant star is received at Earth with an intensity of $2.4\times10^{-8}\ \text{W m}^{-2}$. The star is at a distance of $1.5\times10^{17}\ \text{m}$ from Earth. Assume the star radiates uniformly in all directions and that absorption is negligible. A spectral line from the star is observed at wavelength $6.6\times10^{-7}\ \text{m}$ in vacuum.

A plane longitudinal wave travels to the right in a gas. The frequency of the wave is $680\ \text{Hz}$ and the wave speed is $340\ \text{m s}^{-1}$. Two particles A and B in the gas have equilibrium positions separated by $0.375\ \text{m}$ along the direction of propagation.

X-rays used in medical imaging may have wavelength $1.0\times10^{-10}\ \text{m}$ in vacuum. An X-ray source emits electromagnetic radiation that is directed at a detector after passing through a patient.

The displacement $y$ in metres of particles in a string is modelled by

$y=3.0\times10^{-3}\sin(15.7x-94.2t)$

where $x$ is in metres and $t$ is in seconds. The wave travels in the positive $x$-direction.

A plane sound wave in air is described by a particle displacement

$s=s_0\sin(kx-\omega t)$

The frequency is $1.20\ \text{kHz}$ and the speed of sound is $330\ \text{m s}^{-1}$. The displacement amplitude is $s_0=0.20\ \text{mm}$.

A water wave travels across the surface of a pond. The wave has amplitude $4.0\ \text{cm}$, frequency $0.80\ \text{Hz}$ and wavelength $1.5\ \text{m}$. A small floating cork moves approximately with simple harmonic motion in the vertical direction as the wave passes.