First, let’s look at what this question is asking us to consider. The question wants us to determine the relationship between waves produced from our sine phase base speaker and a cosine phase speaker accidently placed directly across from it. Two important facts come to mind when thinking about this scenario. First, the waves physically overlap in space because the speakers are pointed directly at each other. Second, the sine and cosine waves are exactly 180º out of phase. Remember that waves completely out of phase create destructive interference, meaning that the resultant wave will have no amplitude. The volume directly between the two speakers is zero because volume is directly correlated to wave amplitude.

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 .

Two waves will cancel to zero amplitude when the relative shift between them is half a period. This corresponds to half of , which gives the correct answer of .

Destructive inference occurs when the peak of one wavelength encounters the trough of another wavelength. This causes the waves to cancel each other out, essentially producing a much smaller audible wavelength. In contrast, constructive interference will result in the summation of the wave amplitudes, and an increase in the volume and intensity of the sound.

The capacitance of any capacitor can be calculated with the formula

Since the capacitors are arranged in parallel, the voltage drop across each will be equal, and in this case 10V. Adding capacitors in parallel is the same as adding resistors in series, where the total capacitance of the circuit is equal to the sum of all individual capacitors.

The equation for finding the force on a charge in a magnetic field is

F = qvBsinθ

Where q is charge in coulombs, v is the velocity of the charge, and B is the strength of the magnetic field in Teslas. Since the charge is moving perpendicular to the magnetic field, sinθ =1. Therefore we solve for force by plugging in the values and multiplying.

The force of a charge in a magnetic field is given by the equation . q is the charge, v is the velocity, and B is the magnetic field strength.

Additionally, the force on a current-carrying carrying wire in a magnetic field is given by the equation . I is the current, L is the length or the wire, and B is the magnetic field strength.

Because we assume the angle to be 90^o , we can set the two force equations equal to each other, and derive the equation .

By manipulating the variables, we can generate the equation . None of the other answer choices can be derived from these equations.

We need to find the buoyant force on the sphere to see how much the scale reading changes.

Buoyant force is given by , where V is the volume displaced by the sphere.

We need to find this volume, which also equals the sphere's volume. Given the sphere's mass (m = F/g = 2.94/9.8 = 0.30kg) and density, we can find volume with either  or .

Plugging this volume into the buoyant force equation, together with the density of water (1000 kg/m³) gives the following.

So now the upwards force provided by the scale is reduced by 0.33N.

Using the equation  we can find the frequency of the soundwave. 

In order to solve this problem we must know how to utilize the Doppler formula.

is the velocity of the observer and is the velocity of the source. Notice that the frequency must increase as the observer and source move closer, and therefore the plus sign is used in the numerator and the minus sign is used in the denominator. Had the jogger been moving away from the fire truck, the subtraction function would be used in both the top and bottom.

In this case we see that the source is the fire truck, moving at , and the observer is the jogger, moving at . By plugging these numbers into the formula and  for , we find the perceived frequency or to be .