IB Physics HL Theme C: Wave behaviour questions

A position sensor tracks a component undergoing simple harmonic motion. Its displacement $x$ from equilibrium is modelled by

where the phase angle $\phi$ is in radians. The amplitude is $0.060\ \mathrm{m}$ the period is $0.80\ \mathrm{s}$ and the initial phase angle is $\pi/3$

An oscillator has a period of $2.0\ \text{s}$ Four proposed graphs show its acceleration $a$ against displacement $x$ measured from equilibrium. Which trace is consistent with the oscillator undergoing simple harmonic motion?

A source produces periodic waves in medium X with wavelength $\lambda$ period $T$ and speed $v$ The source is adjusted to produce waves with period $T/2$ in medium Y, where their speed is $3v$ What is the wavelength of the waves in medium Y?

A travelling wave P has frequency $f$ and wavelength $\lambda$ A second travelling wave Q has the same speed as P and a frequency of $2f$ In Q, particles oscillate parallel to the direction of travel. Which description of Q is correct?

A cord and a spring each carry a sinusoidal travelling disturbance along the equilibrium $x$-axis. Figure 1 shows the displacement of particles from equilibrium at $t=0$ and $t=0.20\ \mathrm{s}$ plotted against each particle’s equilibrium coordinate $x$ In the upper panel, $y$ is the cord-particle displacement perpendicular to $x$ with positive $y$ upwards. In the lower panel, $u$ is the spring-particle displacement along $x$ with positive $u$ in the $+x$ direction. Each disturbance retains its profile as it travels.

A monochromatic beam illuminates two identical slits, each of width $a$ whose centres are separated by $d$ The ratio $d/a$ is an integer greater than 1. Which order of the two-slit interference pattern is absent because it coincides with the first minimum of the single-slit diffraction envelope?

Two loudspeakers, $S_1$ and $S_2$ are connected to the same signal generator and emit sound in phase. Figure 1 shows measured distances from each loudspeaker to three positions on a detector’s path. The path lengths are measured to the nearest $0.01\ \text{m}$

In a laboratory, a laser illuminates both slits of a double-slit plate at normal incidence. The separation of adjacent bright fringes is measured on a screen parallel to the plate. A reference laser has wavelength $600\ \mathrm{nm}$ With the original plate and a screen distance of $1.20\ \mathrm{m}$ the measured fringe separation is $3.00\ \mathrm{mm}$

A string on a musical instrument is fixed at both ends and vibrates in the mode shown in Figure 1.

Two sinusoidal waves, each of amplitude $a$ and wavelength $\lambda$ travel in opposite directions along a string and form a standing wave. There is a displacement node at $x=0$ Points $P$ and $Q$ are at $x=\lambda/12$ and $x=\lambda/3$ respectively. What is the ratio of the oscillation amplitude at $P$ to that at $Q$ and what is the phase difference between their oscillations?

A source emits light with wavelength 600 nm and moves directly away from an observer at $1.5 \times 10^6\ \text{m s}^{-1}$ Take the speed of light as $3.0 \times 10^8\ \text{m s}^{-1}$ What is the magnitude of the relative change in wavelength, expressed as a percentage?

A sound emitter moves uniformly through still air. At one instant, the distance between adjacent wavefronts is 0.646 m ahead of the emitter and 0.714 m behind it. The speed of sound in the air is 340 m s⁻¹. In a second arrangement, the emitter is stationary and a detector moves towards it at the speed found in (a). The emitter has the same frequency in both arrangements.