66 exam-style questions on Standing waves and resonance — topic C.4 of Wave behaviour in the IB Physics syllabus — with answers and explanations. Samples below; the full set is free with an account.
A string of length 0.60 m is fixed at both ends. Waves travel along the string at 120 m s⁻¹. Calculate the frequency of the first harmonic.
Answer: 100 Hz
For a string fixed at both ends the first-harmonic wavelength is 2L = 1.2 m, so f₁ = v/2L = 120/1.2 = 100 Hz.
A pipe is closed at one end and open at the other. Which harmonics can be set up in the air column of the pipe?
Answer: Only odd harmonics
A closed end must be a displacement node and an open end an antinode, which is only possible for odd multiples of the first-harmonic frequency (n = 1, 3, 5, …).
P and Q are two oscillating points on a standing wave. They lie on opposite sides of the same node, each less than a quarter of a wavelength from it. What is the phase difference between the oscillations of P and Q?
Answer: π rad
Points in adjacent loops of a standing wave move in opposite directions at every instant, so they oscillate in antiphase: phase difference π rad.
Adjacent nodes of a standing wave on a stretched wire are separated by 0.40 m. The wire oscillates at a frequency of 425 Hz. Determine the speed of the waves travelling along the wire.
Answer: 340 m s⁻¹
The node-to-node distance is half a wavelength, so λ = 0.80 m and v = fλ = 425 × 0.80 = 340 m s⁻¹.
A pipe of length 0.50 m is open at both ends. The speed of sound in air is 340 m s⁻¹. What is the frequency of the third harmonic of the pipe?
Answer: 1020 Hz
For a pipe open at both ends f₁ = v/2L = 340/1.0 = 340 Hz, so the third harmonic is 3f₁ = 1020 Hz.
Which feature distinguishes a standing wave from a travelling wave?
Answer: The amplitude of oscillation depends on position along the medium
In a standing wave the amplitude varies from zero at nodes to a maximum at antinodes, and no net energy is transferred along the medium.
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