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30 exam-style questions with model answers, plus 40 quick multi-choice questions — every question on the site for this standard, grouped by the 10 pages of notes they come from.
Write a full answer before you reveal the model one — that comparison is where the marks come from. Every block links back to the notes that teach it.
Adjacent nodes on a standing wave are m apart.
Calculate the wavelength of the wave.
A standing wave is set up on a string. Explain how a standing wave is formed, and explain why the points called nodes never move.
A student claims that a standing wave on a string transfers energy from one end of the string to the other, just as a travelling wave does.
Discuss this claim fully. Your answer should compare standing and travelling waves in terms of energy, amplitude and phase, and explain where the energy in a standing wave actually resides.
A string fixed at both ends is m long.
Show that the wavelength of its fundamental is m.
A string m long, fixed at both ends, vibrates in its third harmonic at a frequency of Hz.
Calculate the wavelength and the speed of the waves on the string, and explain how many nodes and antinodes the pattern has.
A guitarist finds that a string sounds flat (too low in pitch). They can either tighten the string or press it against a fret to shorten it.
Explain fully how each action changes the fundamental frequency, referring to the harmonic relationship. Then explain why the note still sounds recognisably like a guitar rather than a different instrument even after these changes.
A pipe open at both ends is m long. The speed of sound is m s−1.
Calculate the fundamental frequency of the pipe.
A closed pipe (one end closed) is m long. The speed of sound is m s−1.
Calculate the fundamental frequency and the frequency of the third harmonic, and explain why the pipe cannot produce a second harmonic.
An open pipe and a closed pipe are both m long. The speed of sound is m s−1.
Calculate the first three frequencies each pipe can produce. Compare the two harmonic series fully, explaining the differences in terms of nodes and antinodes, and explain why the two pipes sound different even when producing notes of the same pitch.
State what is meant by the natural frequency of a system, and state the condition required for resonance to occur.
A tuning fork of frequency Hz is held over a tube closed at one end. As the length of the air column is increased from zero, the sound becomes very loud at one particular length.
Explain why the sound becomes loud at that length, and calculate the length, taking the speed of sound as m s−1.
A footbridge is found to sway alarmingly when a group of people walk across it in step, but not when they walk normally. Engineers consider two solutions: adding stiffening to the structure, or fitting dampers.
Explain fully why walking in step causes the problem, and analyse how each proposed solution would work. Refer to natural frequency, driving frequency, amplitude and damping in your answer.
Two tuning forks of frequency Hz and Hz are sounded together.
Calculate the beat frequency.
A piano string is sounded with a Hz tuning fork and beats per second are heard.
State the possible frequencies of the string, and explain how beats are produced.
A technician is tuning a piano string against a Hz reference. Initially they hear beats per second. After loosening the string slightly, they hear beats per second. They continue loosening until no beats are heard, then loosen a little further and hear beats per second.
Determine the string's frequency at each of the four stages, explaining your reasoning. Then explain why the beat method is more precise than simply comparing the two pitches by ear.
In a two-slit interference experiment, waves arriving at a point on the screen have a path difference of exactly two wavelengths.
State whether a bright or a dark fringe is observed at this point, and give a reason.
A two-slit interference pattern is produced using a laser.
Explain why a bright fringe always appears at the centre of the pattern, and explain why the two slits must be illuminated by the same laser rather than by two separate lasers.
Two loudspeakers m apart are driven by the same signal generator at Hz (speed of sound m s−1). A student walks along a line parallel to the speakers and m away from them, and hears the loudness rise and fall.
Explain fully what determines the positions of the loud and quiet points. Then discuss what would happen to the pattern if (a) the frequency were doubled and (b) one speaker were disconnected, and explain what happens to the sound energy at the quiet positions.
In a two-slit experiment, the slits are mm apart, the screen is m away, and the fringe spacing is mm.
Calculate the wavelength of the light.
Light of wavelength nm passes through two slits mm apart onto a screen m away.
Calculate the distance from the central bright fringe to the third bright fringe. Then state and explain what would happen to this distance if the slit separation were halved.
A student performs a two-slit experiment using a white-light source instead of a laser. They observe a white central fringe, with coloured fringes either side that become increasingly smeared and overlapping further from the centre, until the pattern washes out entirely.
Explain fully why the central fringe is white, why the outer fringes are coloured, and why the pattern eventually washes out. Support your answer with a calculation comparing red ( nm) and blue ( nm) light for slits mm apart on a screen m away.
A diffraction grating has lines per millimetre.
Calculate the grating spacing in metres.
Light of wavelength nm falls on a grating with lines per millimetre.
Calculate the angle of the second-order maximum, and explain why the maxima produced by a grating are sharper than those from a pair of slits.
White light is shone through a diffraction grating with lines per millimetre. Instead of white fringes, a series of continuous spectra is seen either side of a white central maximum.
Explain fully why this happens, and calculate the angular width of the first-order spectrum (taking visible light as nm to nm). Determine whether the first- and second-order spectra overlap, showing your reasoning.
An ambulance with its siren on drives toward a stationary observer.
State whether the observer hears a frequency higher or lower than the emitted frequency, and state what happens to the wavelength reaching the observer.
A train sounds its horn at a constant frequency as it travels away from a stationary observer at constant speed.
Explain why the observer hears a lower frequency than the horn emits, and state what happens to the speed of the sound waves.
A student listening to a racing car pass at high speed claims: "The pitch slides smoothly down as the car goes by, because the sound waves are slowed down by the time they reach me once the car has passed."
Discuss this claim fully. Correct both parts of it, explain what the observer actually hears and why, and explain what would change if the car travelled faster.
A siren emitting Hz moves toward a stationary observer at m s−1. The speed of sound is m s−1.
Calculate the frequency heard by the observer.
A train whistle emits Hz. The train passes a stationary observer at m s−1 (speed of sound m s−1).
Calculate the frequency the observer hears as the train approaches and as it recedes, and explain why the two shifts are not equal in size.
A stationary observer beside a straight road measures the sound of a passing motorcycle. As it approaches they measure Hz, and after it has passed they measure Hz. The speed of sound is m s−1.
Determine the frequency emitted by the motorcycle and its speed. Then explain why the emitted frequency is not simply the average of the two measured frequencies.