Two violinists are playing their "A" strings. Each is perfectly tuned at 440 Hz and under 245 N of tension. If one violinist turns her peg to tighten her A string to 251 N of tension, what beat frequency will result

450.78Hz

Explanation:

The frequency of wave in string is directly proportional to its tension. This is mathematically expressed as

F∝T

F = kT where k is the constant of proportionality

From the formula, k = F/T

F1/T1 = F2/T2 = k

If each violin is perfectly tuned at 440 Hz and under 245 N of tension then F1 = 440Hz, T1 = 245N

To get the frequency if the string A is tighten to 251N of tension,

T2 = 251N, F2 =?

Substituting the given values into the equation above to get F2 we have;

440/245 = F2/251

Cross multiplying

245F2 = 440×251

245F2 = 110,440

F2 = 110,440/245

F2 = 450.78Hz

the independent variable, or the one that is intentionally manipulated is the speed.

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.