This question asks us to determine what would happen to the intensity of a sound wave if a variable could be changed. First, we need to remember the equation for intensity: , where A is the wave amplitude, rho is the density of the medium, f is the frequency of the wave, and v is the velocity of the wave.

This formula is important to understand qualitatively. For the MCAT, it is important to understand how the various factors impact the intensity of a wave. If we wanted to quadruple the intensity, we can see that we could double amplitude or double frequency. Seeing that we want the sound pitch to remain the same, we would want to double the amplitude and not the frequency. The relationship between intensity, frequency, and amplitude is important to understand.

This question asks us to determine what would happen to the intensity of a sound wave if a variable could be changed. First, we need to remember the equation for intensity, , where P is the power of the wave, A is the area,  is the wave amplitude, rho is the density of the medium, f is the frequency of the wave, and v is the velocity of the wave.

This formula is important to understand qualitatively. For the MCAT, it is important to understand how the various factors impact the intensity of a wave. If we wanted to halve the intensity, we can see that we could halve the power of the wave or double the area the wave is hitting; thus, we could double the size of the room, allowing the sound wave to have more room to spread out and increasing the area the wave interacts with.

This question asks us to determine the intensity of a wave, given to us as a comparison of the wave intensity to the intensity of the limit of human hearing. In math terms, we know that the decibel scale is calculated as shown below.

I₀ is the limit of human hearing (10^-12 W/m²).

Regardless of the units measured, a ten-fold decrease in volume equals a  decrease in intensity level.

Here, there is a twenty-fold decrease in sound intensity.

A ten-fold decrease would be a  change, and a hundred-fold decrease would be a  change. A  decrease is closer to a ten-fold decrease than a hundred-fold decrease, hence the decrease in intensity level should be closer to .

When a sound wave contacts a surface, it transfers longitudinal vibration into the solid. Because of the increased density in the solid, these longitudinal compressions actually speed up and increase in wavelength. The frequency of the sound remains constant.

Only some of the sound energy is transferred to the solid, however. When the wave impacts the solid, some of the energy is bounced of the surface and reflected back to the source as an echo. This reduction of energy accounts for the lessened intensity experienced by a listener on the opposite side of the wall. Energy is also lost to internal reflection within the wall.

As sound radiates from a point source, it does so in concentric circles. Therefore, we can calculate the intensity of sound using the following formula:

We simply need to calculate : your distance from the space shuttle.

The shuttle is 500 meters from the ground, and you are 300 meters from its launch point. We can calculate the distance from you to the current position of the shuttle by using the Pythagorean Theorem:

There is no need to take the square root, since it's already in the form we need to do the calculation. Plugging in this value to the original equation, we get:

A harmonic is a standing wave that has certain points (nodes) which do not go through any displacement, and certain points (antinodes) that are moving through maximum displacement during the wave's resonation.

Wavelength is related to harmonic on a string fixed at both ends through the formula , where  is the length of the string and  is the number harmonic. By plugging in the given length and wavelength, we can solve for .

The string must be vibrating at the fourth harmonic.

First, notice that the paragraph above tells us that the wave can be modeled as a pipe with one end closed. This is in contrast to the other possibility, where the wave is modeled as a pipe with two ends open. It is critical to recognize this difference, as the definition of sequential harmonics and the formula used to calculate them changes depending on whether both ends are open or not. In the situation where one end is closed, the harmonics are odd numbers, meaning that the first three harmonics are 1^st, 3^rd, and 5^th. In the situation where both ends are open or both ends are closed, the harmonics are sequential, meaning that the first three harmonics are 1^st, 2^nd, and 3^rd.

This question asks us to incorporate information we learned in the pre-question text and new information in the question. First, we are told that we are looking to calculate a distance where maximal sound is heard, in other words, where the amplitude is at its maximum. This only occurs at an anti-node. 

Additionally, we know that the speaker can be modeled as a one-end closed pipe, meaning that the wavelengths of the harmonics are calculated as .

In a one-end closed pipe model, each harmonic ends with maximal amplitude, so we can find L (the length of the pipe, i.e. where the person standing would hear maximal sound), as we know the fundamental harmonic has n = 1.

In an open-closed pipe, we get only odd harmonics, since there must always be a displacement node at the closed end and a displacement antinode at the open end. So, the first overtone is the same as the third harmonic, which has . Similarly, the second overtone is the fifth harmonic, which has . Using the given value of  in the first overtone to be 300Hz, we find  and .