Sound waves and their qualities

The three physiological properties of sound are pitch, intensity and timbre.

1. a) Associate each property with the physical quantity of the wave that determines it: frequency, amplitude (energy transported) or wave shape.
2. b) Give a musical example of each: two sounds that differ only in pitch, only in intensity, and only in timbre.

The human ear perceives frequencies roughly between $20\ \text{Hz}$ and $20\ \text{kHz}$. The diagram shows the three regions of the acoustic spectrum:

Classify the following sound waves into infrasound, audible sound or ultrasound, and justify the classification:

1. a) $15\ \text{Hz}$ (communication between elephants).
2. b) $440\ \text{Hz}$ (the note "A" of a tuning fork).
3. c) $45\ \text{kHz}$ (echolocation of a bat).
4. d) $3\ \text{MHz}$ (medical ultrasound scan).

A tuning fork vibrates at $440\ \text{Hz}$ (speed of sound in air: $340\ \text{m/s}$).

1. a) Calculate the period of the sound wave generated.
2. b) Calculate its wavelength in air.

Match each application with the type of sound wave it uses (infrasound, audible sound or ultrasound) and justify the choice:

1. a) An ultrasound scan to observe a foetus.
2. b) A bat locating insects in the dark.
3. c) A seismograph recording a distant earthquake.
4. d) A fishing sonar to locate shoals of fish.

A violin and a flute play the same note ($440\ \text{Hz}$) with the same intensity, and yet they can be distinguished perfectly.

1. a) Which property of sound allows this, and with which wave quantity is it related?
2. b) Explain the role of harmonics (frequency components that are multiples of the fundamental frequency) in this difference.
3. c) Draw in your notebook, qualitatively, the expected waveform for each instrument and compare it with that of a pure tone.

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

At $15\ \text{m}$ from a concert loudspeaker, the measured intensity level is $90\ \text{dB}$ (data: $I_0 = 10^{-12}\ \text{W/m}^2$; $\pi = 3,14$).

1. a) Calculate the intensity at that point.
2. b) Assuming isotropic radiation, calculate the power of the loudspeaker using $P = I \cdot 4 \cdot \pi \cdot r^2$.
3. c) Comment on two reasons why the result is only an estimate of the real power (think about absorption by air, directivity of the loudspeaker or reflections from the surroundings).

The sound intensity level is defined as $\beta = 10 \cdot \log \frac{I}{I_0}$, measured in decibels ($\text{dB}$), where $I_0 = 10^{-12}\ \text{W/m}^2$ is the threshold intensity of hearing.

Calculate the intensity level of a sound of $I = 10^{-5}\ \text{W/m}^2$.

A loud conversation has an intensity of $I = 5 \cdot 10^{-6}\ \text{W/m}^2$ (data: $I_0 = 10^{-12}\ \text{W/m}^2$; $\log 5 \approx 0,7$).

Calculate its intensity level in decibels using $\beta = 10 \cdot \log \frac{I}{I_0}$.

A passing lorry produces a level of $80\ \text{dB}$ and a quiet library is at $40\ \text{dB}$.

1. a) Without using a calculator, use the logarithmic definition of intensity level to reason how many times more intense (in $\text{W/m}^2$) the sound of the lorry is compared to that of the library.
2. b) Generalise the result: by what factor is the intensity multiplied for every additional $10\ \text{dB}$?

A point sound source emits with power $P = 0,5\ \text{W}$ uniformly in all directions. The intensity at a distance $r$ is $I = \frac{P}{4 \cdot \pi \cdot r^2}$ (take $\pi = 3,14$). The diagram represents isotropic emission.

Calculate the intensity at $5\ \text{m}$ from the source.

A public address loudspeaker emits sound with a power of $P = 3\ \text{W}$ (data: $\pi = 3,14$; $I_0 = 10^{-12}\ \text{W/m}^2$; $\log 2,4 \approx 0,38$).

1. a) Calculate the intensity at $10\ \text{m}$ from the loudspeaker using $I = \frac{P}{4 \cdot \pi \cdot r^2}$.
2. b) Calculate the intensity level at that point, in decibels.

At $2\ \text{m}$ from a drill, the intensity level is $90\ \text{dB}$ (given: $\log 2 \approx 0,3$).

1. a) Moving away to $4\ \text{m}$, the intensity is divided by $4$: calculate by how many decibels the level decreases and its new value.
2. b) Repeat the calculation for $8\ \text{m}$.
3. c) State the rule of thumb that can be deduced: how many decibels are lost each time the distance to the source is doubled?