Progressive waves

The graph illustrates how the displacement of two distinct waves X and Y changes over time. Wave X has frequency $f$ and amplitude $A$. What are the frequency and the amplitude of wave Y?

Feb/March 2016

The speed $v$ of a transverse wave moving along a uniform string is defined by $v = \sqrt{\frac{Tl}{m}}$, where $T$ is the tension in the string, $l$ denotes its length and $m$ its mass. An experiment is carried out to find the wave speed $v$. The readings are shown in Fig. 1.1.

Feb/March 2016

What approximate value would you give for the speed of sound in air?

Feb/March 2017

How does the amplitude of a wave relate to its intensity?

Feb/March 2017

The diagram depicts two waves, R and S. For wave R, the amplitude is $8\,\text{cm}$ and the period is $30\,\text{ms}$. Determine the amplitude and the period of wave S.

Feb/March 2017

A wave pulse travels along a taut rope in the direction indicated. Which diagram represents how the displacement $s$ of particle $P$ in the rope changes with time $t$?

Feb/March 2018

A wave has period $T$, wavelength $\lambda$ and amplitude $A$. The wave is displayed on a graph of displacement $x$ plotted against distance $d$. Which graph is labelled correctly?

Feb/March 2018

The diagram shows the display of an electromagnetic wave on a cathode-ray oscilloscope. The time base setting is $0.20\ \mu\text{s cm}^{-1}$. Which statement is correct?

Feb/March 2018

A wave has a frequency of $5\,\text{GHz}$. What is the time period of the wave?

Feb/March 2019

A wave with frequency $15\,\text{Hz}$ moves through a medium at $24\,\text{m s}^{-1}$. What phase difference is there between two points separated by $2.0\,\text{m}$?

Feb/March 2020

A sound wave appears on the screen of a cathode-ray oscilloscope, as shown. The time-base setting is $0.50\,\text{ms}$ per division. What is the frequency of the sound wave?

Feb/March 2020

A progressive radio wave travelling in a vacuum has a frequency of $75\,\text{MHz}$. What phase difference exists between two points on the wave separated by $50\,\text{cm}$?

Feb/March 2021

Which statement concerning progressive waves is correct?

Feb/March 2022

A cathode-ray oscilloscope (CRO) is being used to find the frequency of a sound wave. The diagram displays the waveform on the screen. The time-base setting is $5.0\,\text{ms div}^{-1}$. What is the most accurate estimate of the sound wave’s frequency?

Feb/March 2022

Blue whales emit sound waves with frequencies from $10\,\text{Hz}$ to $40\,\text{Hz}$. In seawater, sound travels at approximately $1.5\,\text{km s}^{-1}$. Calculate the approximate range of wavelengths of the sound waves emitted by blue whales.

Feb/March 2024

A light beam has power $P$ and a cross-sectional area of $A$. The wave amplitude in the beam is $X$. The beam is then altered so that its frequency stays the same, but its amplitude becomes $4X$ and its cross-sectional area decreases to $\frac{A}{3}$. What is the power of this new beam?

Feb/March 2024

A progressive wave with frequency $300\ \text{Hz}$ moves at a speed of $600\ \text{m s}^{-1}$. Calculate the phase difference between two points on the wave separated by a distance of $0.50\ \text{m}$.

Feb/March 2025

A sound source emits sound with frequency $f$. It produces sound of wavelength $\lambda$.

May/June 2010

The four graphs show a progressive wave travelling along a stretched string. Graphs A and B illustrate how displacement $d$ changes with distance $x$ along the string at a single moment. Graphs C and D illustrate how displacement $d$ changes with time $t$ at one fixed value of $x$. The markings on the graphs are meant to indicate the wavelength $\lambda$, the period $T$ and the amplitude $a$ of the wave, but just one graph has been labelled correctly. Which graph is labelled correctly?

May/June 2011

A source of sound with constant power $P$ is placed in open space. The sound intensity $I$ at a distance $r$ from this source is given by $I = \dfrac{P}{4 \pi r^2}$. How does the amplitude $a$ of the oscillating air molecules depend on the distance $r$ from the source?

May/June 2011

The diagram displays a wave trace on a cathode-ray oscilloscope. The spacing between adjacent vertical and horizontal gridlines is $1.0\,\text{cm}$. The voltage scale is $4\,\text{V cm}^{-1}$ and the time scale is $5\,\text{ms cm}^{-1}$. What are the amplitude and period of the wave?

May/June 2011

A transverse progressive wave is produced on a string. The graph illustrates how the displacement of one point on this string changes with time. The distance XY on the graph represents the ......1...... of the wave. X and Y have the same ......2...... . Which words correctly fill gaps 1 and 2?

May/June 2011

A source of sound with constant power $P$ is placed in open space. The sound intensity $I$ at a distance $r$ from the source is given by $I = \frac{P}{4\pi r^2}$. How does the amplitude $a$ of the vibrating air molecules depend on the distance $r$ from the source?

May/June 2011

The four graphs depict a progressive wave on a stretched string. Graphs A and B illustrate how displacement $d$ changes with distance $x$ along the string at a single moment. Graphs C and D illustrate how displacement $d$ changes with time $t$ at one fixed value of $x$. The graph labels are meant to indicate the wavelength $\lambda$, the period $T$ and the amplitude $a$ of the wave, but just one graph has been labelled correctly. Which graph is correctly labelled?

May/June 2011

The diagram displays a trace of a wave on a cathode-ray oscilloscope. The vertical and horizontal gridlines are spaced by $1.0\,\text{cm}$. The voltage scaling is $4\,\text{V cm}^{-1}$ and the time scaling is $5\,\text{ms cm}^{-1}$. Calculate the amplitude and period of the wave.

May/June 2011

A transverse progressive wave moves along a stretched string from left to right. Fig. 6.1 shows the shape of part of the string at one instant. The wave frequency is $15\,\text{Hz}$. Use Fig. 6.1 to find:

May/June 2011

Two waves, E and G, are shown. Both waves travel at the same speed. Which statement is correct?

May/June 2012

The diagram presents a displacement-time graph for a progressive wave. What are the wave’s amplitude and frequency?

May/June 2012

A light-meter measures the intensity $I$ of the light falling on it. Theory indicates that $I$ varies inversely as the square of the distance $d$. Which graph of the results is consistent with this theory?

May/June 2012

A surveyor’s instrument sends out a laser pulse. How long does the pulse take to travel from the instrument to a wall $150\,\text{m}$ away, bounce off it, and then return to the instrument?

May/June 2012

X and Y are two points on the water surface in a ripple tank. A source that produces waves with constant frequency starts to create waves, and these then move past X and Y, making them oscillate. What is the phase difference between X and Y?

May/June 2012

The diagram illustrates a displacement-time graph for a progressive wave. Determine the amplitude and frequency of the wave.

May/June 2012

Two waves E and G are shown. These waves travel at the same speed. Which statement is correct?

May/June 2012

A light-meter measures the intensity $I$ of the light incident on it. Theory indicates that $I$ varies inversely with the square of the distance $d$. Which graph of the results supports this theory?

May/June 2012

A light wave with amplitude $A$ falls normally on a surface of area $S$. The power per unit area arriving at the surface is $P$. The amplitude of the light wave is then raised to $2A$. The light is afterwards focussed onto a smaller area $\frac{1}{3}S$. What is the power per unit area on this smaller area?

May/June 2013

A wave travels at $340\,\text{m s}^{-1}$ and has a period of $0.28\,\text{ms}$. What is the wavelength of the wave?

May/June 2013

A wave has a frequency of $5\,\text{GHz}$. Calculate the period of the wave.

May/June 2013

The diagram illustrates two waves X and Y. Wave X has amplitude $8\,\text{cm}$ and frequency $100\,\text{Hz}$. Determine the amplitude and frequency of wave Y.

May/June 2013

For a sound wave, the displacement is $y$ at a distance $x$ from the source at time $t$. Which graph shows the amplitude $a$ and the wavelength $\lambda$ of the wave correctly?

May/June 2013

The wave speed $v$ in deep water is related by $v^2 = \dfrac{g\lambda}{2\pi}$ in which $\lambda$ represents the wavelength of the waves and $g$ denotes the acceleration of free fall. A student records the wavelength $\lambda$ and the frequency $f$ for several of these waves. Which graph ought he to plot so that the result is a straight line passing through the origin?

May/June 2014

To two significant figures, what are the period, frequency and amplitude of the wave shown on the graph?

May/June 2014

A sound wave is made up of a sequence of travelling pressure changes away from the usual, steady air pressure. The graph illustrates these pressure changes for two waves at a single moment in time. Wave 1 has an intensity of $1.6 \times 10^{-6}\ \text{W m}^{-2}$. What intensity does wave 2 have?

May/June 2014

The diagram depicts a vertical section through a water wave travelling from left to right. At which point is the water moving upwards at its greatest speed?

May/June 2014

A cathode-ray oscilloscope (c.r.o.) shows a waveform that represents a sound wave. To find the frequency of the sound wave, which section of the displayed waveform should be measured, and which c.r.o. setting has to be known?

May/June 2014

A small source produces spherical waves. The wave intensity $I$ at a point $P$, which is a distance $r$ from the source, varies inversely as $r^2$. What relationship exists between the wave amplitude $a$ and the distance $r$?

May/June 2014

The screen of a cathode-ray oscilloscope shows the output from an electronic circuit. The time-base is adjusted to $5.0\,\text{ns}$ per division and the Y-gain to $10\,\text{V}$ per division. What is the frequency of the signal?

May/June 2014

What is meant by displacement and amplitude for a wave on the surface of water?

May/June 2014

A wave with frequency $15\,\text{Hz}$ moves through a medium at $24\,\text{m s}^{-1}$. What is the phase difference between two points $2\,\text{m}$ apart?

May/June 2015

A wave with amplitude $a$ has intensity $3.0\,\text{W m}^{-2}$. What is the intensity of another wave with the same frequency but amplitude $2a$?

May/June 2015

A whale emits sound waves at a frequency of $5\,\text{Hz}$. These waves are picked up by a microphone and shown on an oscilloscope. What is the time-base setting on the oscilloscope?

May/June 2015

A sound wave moves at a speed of $330\,\text{m s}^{-1}$ and has a frequency of $50\,\text{Hz}$. What could be a possible separation between two points on the wave with a phase difference of $60^{\circ}$?

May/June 2015

A wave pulse travels along a stretched rope in the direction indicated. Which diagram shows correctly how the displacement $s$ of the particle P in the rope changes with time $t$?

May/June 2015

Two sound waves have frequencies of $250\,\text{Hz}$ and $300\,\text{Hz}$. The speed of sound is $340\,\text{m s}^{-1}$. What is the difference in wavelength between these two waves?

May/June 2016

A microphone linked to the Y-plates of a cathode-ray oscilloscope (c.r.o.) is positioned in front of a loudspeaker. The c.r.o. screen shows the trace. The time-base setting is $0.5\,\text{ms cm}^{-1}$ and the Y-plate sensitivity is $0.2\,\text{mV cm}^{-1}$. What is the frequency of the sound produced by the loudspeaker and what is the amplitude of the trace on the c.r.o.?

May/June 2016

The sound intensity $I$ varies inversely with the square of the distance $x$ from the sound source. This is expressed as $I \propto \frac{1}{x^2}$. At point P, which is a distance $r$ from the source S, air molecules oscillate with an amplitude of $8.0\,\mu\text{m}$. Point Q is located a distance $2r$ from S. Determine the oscillation amplitude of the air molecules at Q.

May/June 2016

A longitudinal wave passes along a long spring. The spring is illustrated at a particular moment. What is the wavelength of the wave?

May/June 2017

A sound wave moves with speed $1500\,\text{m s}^{-1}$ and frequency $2500\,\text{Hz}$. Find the smallest separation between a point of maximum pressure in the wave and a point of minimum pressure.

May/June 2017

The display on a cathode-ray oscilloscope (c.r.o.) shows a sound wave, as illustrated. The c.r.o. time-base is adjusted to $2.5\,\text{ms cm}^{-1}$. What is the frequency of this sound wave?

May/June 2017

A bicycle gear wheel is a disc with 50 ‘teeth’ spaced evenly around its rim. It turns 10 times every second. As the wheel spins, a springy metal strip is made to vibrate by the passing ‘teeth’. The sound produced by the metal strip has a frequency equal to the strip’s vibration frequency. The speed of sound in air is $330\,\text{m s}^{-1}$. What wavelength does the emitted sound have?

May/June 2017

A transverse wave moves along a rope. The graph illustrates how the particles’ displacement varies with distance along the rope at one particular moment. At what distance along the rope do the particles have the greatest upward velocity?

May/June 2017

A transverse progressive wave is established on a string. The graph shows how the displacement of one point on this string varies with time. The distance $XY$ on the graph represents the …1… of the wave. $X$ and $Y$ have the same …2…. Which words correctly fill gaps 1 and 2?

May/June 2018

The diagram illustrates the screen of a cathode-ray oscilloscope (c.r.o.) showing a wave. The time-base on the c.r.o. is adjusted to $10\ \text{ms\ per division}$. What is the frequency of the wave?

May/June 2018

A displacement-distance graph for a transverse progressive wave is displayed. The phase difference between points $X$ and $Y$ may be written as $(180n)^{\circ}$. What is the value of $n$?

May/June 2018

The four graphs show a progressive wave travelling along a stretched string. Graphs A and B illustrate how displacement $d$ changes with distance $x$ along the string at a single instant. Graphs C and D illustrate how displacement $d$ changes with time $t$ at one fixed value of $x$. The markings on the graphs are meant to indicate the wavelength $\lambda$, the period $T$ and the amplitude $a$ of the wave, but just one graph has been labelled correctly. Which graph is correctly labelled?

May/June 2018

A cathode-ray oscilloscope (c.r.o.) is being used to find the frequency of a sound wave. The diagram displays the waveform on the screen. The time-base setting is $5.0\,\text{ms/div}$. Determine the frequency of the sound wave.

May/June 2018

For a progressive wave, state the meaning of the period.

May/June 2018

A transverse wave travelling through a medium has the waveform shown, where $y$ represents vertical displacement and $x$ represents horizontal distance. The wave moves at a speed of $20.0\ \text{cm s}^{-1}$. A particle in the medium vibrates vertically. Which graph of vertical displacement $y$ against time $t$ most closely shows the motion of this particle?

May/June 2019

A whale emits sound waves with frequency $5\,\text{Hz}$. The waves are picked up by a microphone and shown on an oscilloscope. What value should be chosen for the oscilloscope time-base?

May/June 2019

The diagram shows the arrangement of particles in a progressive sound wave at one particular moment. The wave travels with speed $v$. $P$ and $Q$ are two positions in the wave separated by a distance $L$. Which expression gives the wave’s frequency?

May/June 2019

A wave travels across the water surface. The diagram illustrates how displacement $s$ changes with distance along the wave at time $t = 0$. Which graph most accurately represents how the displacement $s$ of point $P$ on the wave varies with time $t$?

May/June 2019

A cathode-ray oscilloscope (CRO) is employed to show the trace produced by a sound wave. The time-base is adjusted to $5\,\mu\text{s mm}^{-1}$. What is the frequency of the sound wave?

May/June 2019

The graph illustrates how displacement $y$ changes with distance $x$ along a progressive wave at a particular instant. What is the phase difference between points P and Q on the wave?

May/June 2019

Wave-power generators make use of the energy carried by waves moving across the ocean surface. A wave’s energy depends on its amplitude. What is the correct meaning of amplitude?

May/June 2019

A sound wave with frequency $270\,\text{Hz}$ is displayed on a cathode-ray oscilloscope (CRO). The CRO waveform is shown. What is the time-base setting on the CRO?

May/June 2019

Define the term velocity.

May/June 2019

As it travels through air, a sound wave becomes less intense while its frequency remains constant. Which statement is the correct one?

May/June 2020

The graph shows how the displacement of an electromagnetic wave at one point varies with time. The wave is moving through a vacuum. What are the amplitude and the wavelength of the wave?

May/June 2020

A transverse wave travels along a rope. Two points X and Y on the rope are separated by a quarter of a wavelength. Which statement about the two points X and Y cannot be true at any moment?

May/June 2020

Two progressive waves are incident at a stationary point P. The graph shows how the displacement of each wave at point P changes with time. What is the phase difference between the two waves at point P?

May/June 2020

A microphone that is linked to the Y-plates of a cathode-ray oscilloscope (CRO) is positioned in front of a loudspeaker. The CRO screen shows the trace. The time-base setting is $0.5\,\text{s cm}^{-1}$ and the Y-plate sensitivity is $0.2\,\text{mV cm}^{-1}$. Determine the frequency of the sound produced by the loudspeaker and the amplitude of the CRO trace.

May/June 2020

Two progressive waves overlap at one point. What condition has to be satisfied for superposition of the waves to take place?

May/June 2020

A wave with amplitude $A$ has intensity $I$. When it travels through a particular medium, its intensity becomes $\dfrac{I}{4}$. What is the wave’s new amplitude?

May/June 2020

A wave moves along a coiled spring. The graph shows how the displacement of a point on the spring changes with time. What is the frequency of the wave?

May/June 2020

At a fixed point P, progressive sound waves Y and Z meet. Figure 4.1 shows how the displacement $x$ of each wave at P changes with time $t$.

May/June 2020

In a progressive wave, two particles are separated by $10\,\text{cm}$. The two graphs illustrate how the displacement $d$ of each particle changes with time $t$. What situation could the two graphs represent?

May/June 2021

A microphone, linked to a cathode-ray oscilloscope (CRO), detects a sound wave. The CRO screen shows a waveform, as illustrated. The time-base is adjusted to $20\,\mu\text{s div}^{-1}$. What is the frequency of the sound wave?

May/June 2021

A transverse progressive wave with wavelength $\lambda$ is produced on a stretched string. The graph illustrates how displacement $y$ varies with distance $x$ at one specific instant. The wave has displacement $+y_1$ when $x = \dfrac{\lambda}{8}$. What are the next two values of $x$ at which the displacement $y$ is once more equal to $+y_1$?

May/June 2021

The graph illustrates how the displacement of an air particle changes with time as a progressive sound wave moves through the air. The speed of sound in air is $330\,\text{m s}^{-1}$. What wavelength does the wave have?

May/June 2021

A microphone is attached to a cathode-ray oscilloscope (CRO). The microphone detects a sound wave that has a constant frequency. The CRO screen is displayed. The time-base is adjusted to $1.0\,\text{ms cm}^{-1}$. What is the frequency of the sound wave?

May/June 2021

The graph illustrates how the displacement of a particle changes with time as a progressive wave moves through it. What are the wave’s frequency and amplitude?

May/June 2022

The graph indicates how the displacement of an air particle changes with time as a sound wave moves through air. The sound intensity is reduced to half, while the frequency stays the same. The four graphs below are drawn on the same scale as the graph above. Which graph represents the displacement of the air particle?

May/June 2022

Which statement is true for every type of progressive wave?

May/June 2022

A sound wave moves from left to right through a room. The change, with distance across the room, in the displacement of the air molecules at one instant is shown. At what distance is the air pressure at its lowest?

May/June 2022

The way in which the displacement $y$ of a transverse wave on a rope varies with distance $x$ is shown at time $t = 0$. The wave has frequency $0.5\,\text{Hz}$. A point P on the rope is labelled. The diagram shows P in its initial position and also four possible new positions. What is the position of P at time $t = 1\,\text{s}$?

May/June 2022

A microphone that detects sound of constant frequency is linked to a cathode-ray oscilloscope (CRO). The trace displayed on the CRO screen is shown. Which property of the sound wave can be measured using only the information from the CRO?

May/June 2022

In an experiment, a student uses a microphone together with a cathode-ray oscilloscope (CRO) to investigate a sound wave. The diagram shows the trace displayed on the CRO screen. The student expects a sinusoidal waveform to appear on the screen. Which changes should the student make to the time-base and the $y$-gain of the CRO so that the screen displays a continuous trace for one complete cycle of the waveform?

May/June 2023

The graph illustrates how the displacement of a particle in a progressive wave changes with time. Two readings, $x$ and $y$, are marked on the graph. What do $x$ and $y$ stand for?

May/June 2023

Two progressive waves arrive together at a point. What condition has to be satisfied for superposition of the waves to occur?

May/June 2023

A microphone picks up a sound wave. The microphone is linked to a cathode-ray oscilloscope (CRO). The pattern of the trace shown on the CRO screen is shown. Which property of the sound wave can be found by using only a horizontal measurement on the screen and the value of a CRO control setting?

May/June 2023

A progressive wave has a frequency of $1.5\,\text{kHz}$ and moves through a medium with a speed of $340\,\text{m s}^{-1}$. What is the smallest distance between two points on the wave that are separated by a phase difference of $70^{\circ}$?

May/June 2023