## Sound Intensity

**1. **Brazilian law prohibits the use of horns in regions near hospitals, schools and in tunnels. If a driver honks within a tunnel with a sound intensity level of 90dB, given that the default tunnel intensity is LSA.

If 10 drivers honk inside a tunnel simultaneously with the same loudness, what is the loudness level inside the tunnel?

*To solve this problem we must consider the equation that describes the intensity of the sound level, ie:*

*Recalling that the sound intensity equivalent to the audible sensation threshold (SAI) is equal to:*

*Using this data and what has already been said in the problem we can calculate what will be the sound intensity of each horn:*

*Knowing the intensity of each horn we can find out the resulting intensity of 10 horns working simultaneously:*

*Then just calculate the sound intensity level for the 10 horns:*

If the student did not understand the properties of the logarithms used, see:

//www.somatematica.com.br/emedio.php

## Sound tubes

**1.** In the Kundt tube, illustrated below, a sound source emits sound at a frequency of 825Hz. Inside the tube there is an amount of cork dust, which accumulates at distances of 20cm. What is the speed of sound wave propagation in the pipe?

*The 20cm distance quoted in the problem equals the distance between two nodes of the sound wave, because at these points the wave "leaves" vacant space for matter to accumulate. Knowing that the wavelength equals the distance between 3 nodes, we conclude that the sound wavelength is 40cm**. Knowing this, just calculate the propagation speed, since we know the frequency:*

## Doppler Effect

**1.** A bullet train whistles past a station platform. A person standing on the platform hears the whirring frequency of 450Hz. After the train passes, the whistle frequency seems to drop to 300Hz. How fast does the bullet train run? It considers sound speed equal to 340m / s.

*Using the generalized Doppler effect equation:*

*In the first case, when the train approaches and the observer remains stationary:*

*In the second case, when the train departs and the observer remains stationary:*

*To find the train speed we can isolate the frequency of the whistle sound and solve the equation, or we can divide one equation by another:*