A standing wave is produced on a horizontal string. Adjacent nodes are separated by $0.18\ \text{m}$. The driving frequency is $95\ \text{Hz}$.

A string of length $0.72\ \text{m}$ is fixed at both ends. The speed of transverse waves on the string is $58\ \text{m s}^{-1}$.

A student drives a lightly damped mass-spring system using a motor. The driving frequency can be varied while the driving force amplitude is kept constant.

A string fixed at both ends is driven at a frequency that produces a clear standing wave. The graph shows the transverse displacement of the string at one instant. A dashed curve shows the string half a cycle later.

A short pulse is sent along a string towards a boundary. The images show the incident pulse and the reflected pulse for two different boundary conditions.

A mass attached to a spring is displaced and released. The displacement-time graphs show the motion for three different damping conditions.

A pipe of length $0.60\ \text{m}$ is closed at one end and open at the other. The speed of sound in air is $330\ \text{m s}^{-1}$. End corrections are negligible.

The displacement-time graphs show the return to equilibrium of the same oscillator after being displaced and released with three different damping conditions.

A standing wave on a string has nodes at $x=0$, $x=0.40\ \text{m}$ and $x=0.80\ \text{m}$. Points A and B are in the first loop at $x=0.10\ \text{m}$ and $x=0.30\ \text{m}$. Point C is in the next loop at $x=0.50\ \text{m}$.

A flexible rod of length $1.20\ \text{m}$ is supported at its centre so that both ends are free to move. Transverse waves travel along the rod at $240\ \text{m s}^{-1}$.

Two pipes have the same length $L$ and contain air at the same temperature. Pipe A is open at both ends. Pipe B is closed at one end and open at the other.

A model of the greenhouse effect treats a molecule in the atmosphere as a system with allowed vibrational modes. Infrared radiation from Earth is incident on the molecule.

A student investigates the resonant frequencies of a stretched string fixed at both ends. The length of the vibrating section is $0.72\ \text{m}$.

A pipe is closed at one end and open at the other. A loudspeaker drives the air in the pipe. The speed of sound is $340\ \text{m s}^{-1}$.

A driven oscillator is tested with three different damping arrangements. The graph shows the steady-state amplitude as the driving frequency is varied.

The graph shows the steady-state amplitude of a driven oscillator as a function of driving frequency for two different damping conditions. The curves are schematic and not to exact scale.

Barton’s pendulums are used to demonstrate resonance. A heavy driver pendulum of length $0.64\ \text{m}$ shakes a horizontal support. Several lighter pendulums of different lengths hang from the same support. Take $g=9.8\ \text{m s}^{-2}$.

A flexible rod of length $0.60\ \text{m}$ is supported at its centre and has nodes at both ends. A motion sensor records the positions of minimum amplitude along the rod for one resonant mode.

Two pipes of the same length are driven by the same loudspeaker. Pipe A is open at both ends. Pipe B is closed at one end and open at the other. The speed of sound is constant.

Barton pendulums are set up with a heavy driver pendulum attached to a horizontal support. Several lighter pendulums of different lengths hang from the same support. The maximum amplitude reached by each pendulum after the driver has been set oscillating is recorded.

A lightly damped oscillator is driven sinusoidally. The phase difference between the displacement of the oscillator and the displacement of the driver is measured at different driving frequencies. The amplitude response is measured at the same time.

A horizontal string of length $1.20\ \text{m}$ is fixed at both ends and is driven by a vibration generator. At one driving frequency the string forms a steady pattern with three equal loops. The wave speed on the string is $96.0\ \text{m s}^{-1}$.

A plastic pipe of length $0.850\ \text{m}$ is closed at one end and open at the other. The speed of sound in air is $340\ \text{m s}^{-1}$. End corrections are not required.

A door closer is tested after the door is displaced slightly from its equilibrium position and released. Three possible displacement-time graphs are shown for the return motion.

Barton’s pendulums are used to demonstrate resonance. A heavy driver pendulum of length $0.640\ \text{m}$ is made to oscillate and drives a horizontal support. Four light pendulums of different lengths hang from the same support. The gravitational field strength is $9.81\ \text{N kg}^{-1}$.

The infrared absorption spectrum of a gas sample is compared with the spectrum of infrared radiation emitted by Earth’s surface. The absorption is modelled as resonance of molecular vibration modes.

A rotating machine is mounted on a platform. The graph shows the vibration amplitude of the platform as the rotation frequency of the machine is slowly increased. Engineers then add a damping pad and repeat the test.

A small building component is forced to vibrate by a motor. The graph shows how its steady-state amplitude varies with the driving frequency for two different amounts of damping.

A loudspeaker faces a rigid vertical wall. A microphone is moved along the line between the loudspeaker and the wall. The speed of sound in air is $340\ \text{m s}^{-1}$.

A string of length $0.900\ \text{m}$ has one end fixed to a support and the other end attached to a frictionless light ring that can move vertically. The wave speed on the string is $54.0\ \text{m s}^{-1}$.

A uniform flexible rod of length $0.750\ \text{m}$ is free at both ends. It is supported at its centre by a very light thread and is made to vibrate longitudinally. The speed of waves in the rod is $3.00\times 10^3\ \text{m s}^{-1}$.

A standing transverse wave is set up on a string. The diagram shows one instant of the string and four labelled points A, B, C and D. Points A and B are in the same loop. Points C and D are in adjacent loops separated by a node.

Infrared radiation emitted by Earth’s surface passes through the atmosphere. Some gas molecules absorb strongly only in particular infrared frequency ranges.

A laboratory platform is mounted on springs. A rotating machine on the platform exerts a periodic force at $3.00\ \text{Hz}$. The effective spring constant is $180\ \text{N m}^{-1}$ and the oscillating mass is $0.500\ \text{kg}$ before equipment is added.

Two organ pipes have the same length, $0.680\ \text{m}$. Pipe A is open at both ends. Pipe B is closed at one end and open at the other. The speed of sound in air is $340\ \text{m s}^{-1}$. End corrections are not required.