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Wave Systems · Part 1 of 3
15 exam-style questions with model answers, plus 20 quick multi-choice questions — every question on this part of the standard, grouped by the 5 pages of notes they come from.
Write a full answer before you reveal the model one. That comparison is where the learning happens.
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.