General Wave Properties: Physics 0625 (Cambridge O Level / IGCSE)

A car's rear parking-sensor unit emits a train of ultrasonic sound pulses to detect obstacles behind the vehicle. The sensor operates at a frequency of $40\text{ kHz}$, and sound travels through the air at $340\text{ m/s}$. Calculate the wavelength of the ultrasonic pulses, giving your answer in mm.

A bottling-factory technician notices that the flat rubber conveyor belt carrying glass bottles has developed a travelling ripple fault along its surface, caused by a worn support roller. The ripple pattern moves continuously along the length of the belt.

(a) Using a strobe light, the technician freezes the belt's motion and measures the distance from one ripple crest to the next crest as $0.24\text{ m}$, and the height of each ripple crest above the flat resting level of the belt as $3.0\text{ mm}$. State the wavelength and the amplitude of this ripple wave. [2]

(b) Using a stopwatch, the technician then times $15$ complete ripple cycles passing a fixed point on the belt in $6.0\text{ s}$. Calculate the frequency of the ripple wave. [2]

(c) Calculate the speed at which the ripple wave travels along the belt. [2]

(d) State whether this wave on the belt is transverse or longitudinal, and justify your answer in terms of the direction the belt material moves compared with the direction the wave travels. [2]

A water-sports training centre has a large wave pool used to train surfers. Paddle-generated swell waves start out in deep water at one end of the pool, then cross onto a gently sloping shelf where the water becomes much shallower, before some of the waves travel on to strike a solid vertical wall at the far end of the pool.

(a) State what happens to the speed of the swell waves as they cross from the deep water onto the shallow shelf, and use this, together with the idea of wavefronts, to explain why the waves change direction (refract) as they cross the boundary at an angle. [3]

(b) The frequency of the swell does not change as the waves cross from deep to shallow water. State what happens to the wavelength of the waves as their speed decreases, and explain why, referring to the equation $v = f\lambda$. [2]

(c) Some of the swell waves travel on to strike the vertical wall and bounce back across the pool. State what happens to the wavelength and to the frequency of a wave when it reflects from the wall, compared with the wave arriving at the wall. [2]

A large open-air stadium concert is held next to a quiet residential street. The stadium's boundary is a continuous solid wall, except for a single wide opening where sound can pass directly through to the street outside. The music reaching this opening contains low-frequency bass notes with a wavelength of about $2.0\text{ m}$, and high-frequency treble notes with a wavelength of about $0.20\text{ m}$. The opening itself is $2.5\text{ m}$ wide.

(a) State the condition, in terms of wavelength and gap width, needed for a wave to diffract strongly as it passes through a gap. [1]

(b) Using this condition, state and explain which of the two types of sound, the bass notes or the treble notes, diffracts more strongly through the opening, spreading out into a much wider area of the street beyond. [2]

(c) A sound engineer wants to redesign the opening so that the treble notes ALSO diffract strongly through it. State one change she could make to the width of the opening, and explain why this would achieve her aim. [2]

At an adventure park, a taut steel zip-line cable stretches between two towers. A gust of wind makes one end of the cable flick briefly up and down, sending a wave pulse travelling horizontally along the cable towards the far tower. Separately, a cyclist uses a hand pump to inflate a tyre: each stroke of the pump forces a pulse of compressed air along the flexible connecting hose, alternating with pulses of less compressed air, until the pulses reach the tyre valve. Which row correctly identifies the type of each wave?

A speedboat crosses a calm lake, leaving behind a wake of parallel ripples on the water surface. Successive ripple crests are measured to be $80\text{ cm}$ apart, and the ripples are found to travel across the lake at $2.4\text{ m/s}$. Calculate the frequency of the ripples.

A construction site sounds a warning siren before each scheduled blast. An observer stationed $680\text{ m}$ away sees the flash of the warning light (which arrives essentially instantly) and starts a stopwatch, stopping it the moment the sound of the siren reaches her. The stopwatch reads $2.0\text{ s}$.

(a) Calculate the speed of the sound wave as it travels from the siren to the observer. [2]

(b) The siren is stated by its manufacturer to produce sound at a frequency of $200\text{ Hz}$. Using your answer to part (a), calculate the wavelength of the sound wave. [2]

(c) State whether the sound wave travelling through the air is transverse or longitudinal, and justify your answer in terms of the direction air particles vibrate compared with the direction the wave travels. [1]

A seismograph at a monitoring station records ground vibrations from a distant earthquake. Two types of seismic wave arrive at the station:

• Primary (P) waves, in which rock particles vibrate back and forth along the same direction that the wave travels.
• Secondary (S) waves, in which rock particles vibrate from side to side, perpendicular to the direction the wave travels.

(a) State, with a reason based on the descriptions above, whether P-waves are transverse or longitudinal. State, with a reason, whether S-waves are transverse or longitudinal. [2]

(b) The P-wave arriving at the station has a frequency of $2.0\text{ Hz}$ and travels through the rock at a speed of $6.0\text{ km/s}$. Calculate the wavelength of this P-wave, giving your answer in km. [3]

(c) The S-wave from the same earthquake has a wavelength of $1.2\text{ km}$ and travels through the rock at a speed of $3.6\text{ km/s}$. Calculate the frequency of this S-wave. [3]

Ocean swell waves with a wavelength of $12\text{ m}$ approach the entrance to a small harbour. The width of the gap between the two harbour walls can be altered. Which gap width would cause the incoming swell to diffract most strongly, spreading out widely once inside the harbour?

In a ripple tank demonstration, a straight vibrating bar produces straight, parallel wavefronts that travel across the water and strike a flat metal barrier placed across one end of the tank.

(a) State what a wavefront represents in terms of the vibration of the water surface. [1]

(b) The vibrating bar is driven by a motor at a stated frequency of $5.0\text{ Hz}$. Before reaching the barrier, the wavefronts are measured to be $3.0\text{ cm}$ apart. Calculate the speed of the waves in the ripple tank, giving your answer in m/s. [2]

(c) State what happens to the wavelength, frequency and speed of the waves as they reflect from the barrier, compared with their values before reflection, and describe one measurement the technician could make on the reflected wavefronts to confirm that the frequency has not changed. [3]