The nature of waves

A cork floats in the sea and a series of waves passes beneath it on their way to the shore.

1. a) Does the cork travel with the waves to the beach, or does it simply move up and down, remaining in almost the same spot?
2. b) If the water does not move forward with the wave, what is it that actually reaches the shore?

Classify each of these waves as mechanical (requires a material medium to propagate) or electromagnetic (can travel through a vacuum), and write out all six complete classifications:

1. a) Sound in air.
2. b) Sunlight.
3. c) Sea waves.
4. d) Radio waves.
5. e) The wave travelling along a guitar string.
6. f) X-rays.

Which of them could cross the space between the Earth and the Moon?

Andrea shakes the end of a rope up and down and a wave moves along it. Afterwards, she pushes a coil of a stretched spring and a compression travels through the spring. The figure represents both waves.

1. a) Which of the two waves is transverse and which is longitudinal?
2. b) Explain the difference by looking at how each point of the medium moves compared to the direction in which the wave travels.
3. c) Sound causes air to oscillate in the same direction in which it travels: to which type of wave does it belong?

The waves that a duckling generates while swimming in a pond travel at $1,2\ \text{m/s}$, and the duckling produces $0,6$ waves per second.

1. a) What is the frequency of the waves?
2. b) Calculate their wavelength using $v = \lambda \cdot f$.

At the beach, Aitana observes that the wave crests arrive separated by $4\ \text{m}$ from one another and that each crest rises $0,6\ \text{m}$ above the calm water level. The figure represents the waves she observes.

1. a) What is the wavelength $\lambda$?
2. b) What is the amplitude $A$ of the waves?

Sitting on a buoy, a swimmer counts that $15$ crests pass by in $30\ \text{s}$.

1. a) Calculate the frequency $f$ of the waves in hertz.
2. b) Explain in your own words what this frequency value means.

$10$ crests pass a buoy in $4\ \text{s}$, and a photograph shows that two consecutive crests are separated by $0,6\ \text{m}$.

1. a) Calculate the frequency of the waves.
2. b) Calculate their wave speed.

An anchored boat rocks $30$ times per minute due to the waves.

1. a) Express its frequency in hertz.
2. b) Calculate the period of the rocking.

The alternating current supplying domestic sockets changes direction with a period of $0,02\ \text{s}$.

1. a) Calculate its frequency in hertz.
2. b) How many complete cycles occur in one minute?

A tsunami in the open ocean travels at about $720\ \text{km/h}$ and its period is about $20\ \text{min}$. The figure shows a diagram of the tsunami wave in the open ocean.

1. a) Express its speed in $\text{m/s}$.
2. b) Express its period in seconds.
3. c) Calculate its wavelength and express it in kilometres.
4. d) In the open ocean, the height of the wave is less than $1\ \text{m}$, spread over that enormous wavelength: explain why ships barely notice the tsunami in the open sea even though it carries a gigantic amount of energy.

Earthquakes emit P-waves (longitudinal) travelling at $6\ \text{km/s}$ and S-waves (transverse) travelling at $3\ \text{km/s}$. At a seismic station, the S-wave arrives $50\ \text{s}$ after the P-wave. The diagram shows the focus of the earthquake and the station.

1. a) If the focus of the earthquake is at a distance $d$ from the station, write down the time taken for each wave to arrive.
2. b) Set up the equation $t_S - t_P = 50$ and calculate the distance $d$ to the focus.
3. c) Check the result by calculating the travel time of each wave.