Types of wave motion

Classify the following waves as mechanical or electromagnetic and explain the criterion you have used:

1. a) The sound emitted by a loudspeaker.
2. b) The light from a lighthouse.
3. c) The microwaves in an oven.
4. d) Ocean waves.
5. e) Seismic waves from an earthquake.

In $2015$, the LIGO observatory detected gravitational waves for the first time, coming from the merger of two black holes located $1,3\cdot10^{9}$ light years away. Gravitational waves travel through a vacuum at $c = 3\cdot10^{8}\ \text{m/s}$. Data: $1$ light year $= 9,46\cdot10^{15}\ \text{m}$; $1$ year $= 3,156\cdot10^{7}\ \text{s}$.

1. a) Express the distance to the source in metres, in standard form.
2. b) Calculate the time the signal travelled before reaching Earth, in seconds.
3. c) Reason whether gravitational waves are electromagnetic or mechanical waves and what distinguishes them from both.

Explain the difference between a transverse wave and a longitudinal wave, indicating how the medium oscillates in each case relative to the direction in which the disturbance travels, and give a real-life example of each type.

Seismic P-waves are longitudinal and seismic S-waves are transverse.

1. a) Explain what each of these statements means, describing how the ground moves as each type of wave passes.
2. b) Reason which of the two types cannot propagate through the fluid layers of the Earth's interior and why.

A piano string of length $1\ \text{m}$ has a mass of $10\ \text{g}$ and is subjected to a tension of $400\ \text{N}$.

1. a) Calculate its linear density $\mu$, in $\text{kg/m}$.
2. b) Calculate the propagation speed of transverse waves in the string using $v = \sqrt{\frac{T}{\mu}}$.
3. c) Calculate the time taken for a pulse to travel along the string from one end to the other.

A sharp blow is struck at the end of a steel pipe of length $1000\ \text{m}$, filled with water and surrounded by air, so that sound travels through all three media simultaneously. The speeds of sound are $5100\ \text{m/s}$ in steel, $1480\ \text{m/s}$ in water and $340\ \text{m/s}$ in air.

1. a) Calculate the time taken for the sound to reach the other end through each of the three media.
2. b) Explain why three separate signals are perceived in time at the other end.
3. c) Reason, relating it to the internal structure of each medium, why sound travels faster in a solid than in a gas.

In the open sea, a tsunami propagates as a gravity wave whose speed depends on the depth $h$ according to $v = \sqrt{g \cdot h}$. Take $g = 9,8\ \text{m/s}^2$.

1. a) Calculate the speed of the tsunami in an area of the ocean with a depth of $4000\ \text{m}$, in $\text{m/s}$, and express it in $\text{km/h}$.
2. b) Calculate the time it would take to cover $2000\ \text{km}$ of open ocean at that speed, in hours.
3. c) As it approaches the coast, the depth decreases: reason what happens to the tsunami's speed and explain, using the conservation of energy transported by the wave train, why its height increases on reaching the coast.

When a guitar string fixed at both ends is plucked, a standing wave is formed as shown in the figure.

1. a) Explain what nodes and antinodes of a standing wave are.
2. b) State, in terms of the wavelength $\lambda$, the distance separating two consecutive nodes.

A standing wave with four antinodes is formed on a string of $1,2\ \text{m}$ fixed at both ends.

1. a) Draw the shape of the string in your notebook and mark the nodes and antinodes.
2. b) Calculate the wavelength, taking into account that four half-wavelengths fit on the string.
3. c) If waves travel along the string at $240\ \text{m/s}$, calculate the frequency of the vibration.

You can do it on paper and send a photo with your answer.

A guitar string of length $0,65\ \text{m}$ vibrates in its fundamental mode, that is, with a single antinode between the two fixed ends. Waves travel along it at $260\ \text{m/s}$.

1. a) Reason, from the fixed-end condition, that the wavelength of the fundamental mode is $\lambda_1 = 2 \cdot L$.
2. b) Calculate the fundamental frequency using $f_1 = \frac{v}{2 \cdot L}$.