The question asks us to determine how long it will take for a wave beat to reach an audience member at 100m away; thus, we need to calculate the velocity of the wave to determine the time.

We know from kinematics that . This can be rearranged to solve for t: .

The velocity of a wave can be obtained with the formula , where  is the tension in the string and is the mass per unit length of the string. Since the tension is quadrupled, the velocity will be doubled.

Let's assume that a string with tension and a mass per unit length produces a wave with velocity .

If we increase the tension by a factor of four, we will get the below expression.

We can see that , and we know that .

A photon will travel fastest through a vacuum. Photons are generally massless and can be thought of as a light wave, which travels fastest in a vacuum and slowest through a metal or solid. This can be visualized using the concept of the index of refraction, which describes the speed of light through air compared to the speed through other mediums. A vacuum will be the least dense and cause the least hindrance to a photon as it travels, thus giving it the lowest index of refraction and allowing the fastest speed of light.

If there are 500 waves over a distance of 100 meters, we can say that the wavelength is:

Now we can use the formula for the speed of waves:

The speed of sound is dependent on the temperature of the transmitting medium. The speed of light is not.

Use the equation:

Focal length is negative for convex mirrors, and image distance is negative for virtual images. We are given these values in the question, allowing us to calculate the object distance.

When an object is placed a distance from a converging lens or mirror that is equal to the focal length, no image is produced. To test this out, stand in front of a single concave mirror and continue to back up until you no longer see an image. Once you've reached this point, you will be standing one focal length away from the mirror. 

When the object is less than one focal length away from the converging lens/mirror, the image will be virtual and upright.  

If you don't have these trends committed to memory, you can derive them from the equation .

When  is a negative integer the image is virtual, and when it is a positive integer the image is real.

First we need the object and image distances away from the eyeglass lenses. Here, the newspaper is the object and the  focal point is where the image needs to be located. Find the distance from the object to the lens, and the distance of the image to the lens, by subtracting out the distance from the lens to the eye.

Now apply the thin lens equation to determine focal length.

Recall that if the image is on the same side of the lens as the object, then image distance is negative.

Relevant equations:

Step 1: Find the focal length of the mirror.

Step 2: Plug this focal length and the object distance into the lens equation.

Relevant equations:

Step 1: Find the focal length of the mirror (remembering that convex mirrors have negative focal lengths, by convention).

Step 2: Find the image distance using the thin lens equation.

Step 3: Use the magnification equation to relate the object distances and heights.