If you solve an equation and the answer is expressed in watts, what are you solving for?
if they actually show it
frequency determines the pitch we perceive. amplitude determines the volume, and loudness perceived (see more detail below)
a most fundamental wave shape is the sine (or cosine). a sine wave has three parameters: (1) frequency, (2) phase, and (3) amplitude. out of the three, two play a role in your question, as follows.
the frequency, namely the number of periods (repetitions) per second, is perceived by our ear of "the pitch." the higher the frequency, the higher the pitch. however, our ears perceive pitch as a logarithm of the physical frequency. every doubling of the frequency causes us to hear the pitch to increase by one octave.
the volume is determined by the amplitude of the wave. the higher the amplitude (positive or negative) the higher the volume. our ears perceive volume as "loudness" and, again, not linearly - some frequencies are perceived as louder than others, even though they have the same physical volume. frequencies between about 200 and 2000 hz are perceived as louder than the rest of the audible spectrum (between 20 and 20000 hz).
interestingly, the phase does not play all too prominent role in perception, at least as far as music and speech are concerned.
“without loss of generality, we only need to look at the equation for the x-position, since we know that centripetal acceleration points towards the center of the circle. thus, when θ = 0, the second derivative of x with respect to time must be the centripetal acceleration.
the first derivative of x with respect to time t is:
dx/dt = —rsinθ(dθ/dt)
the second derivative of x with respect to time t is:
d2x/dt2 = —rcosθ(dθ/dt)2—rsinθ(d2θ/dt2)
in both of the above equations the chain rule of calculus is used and by assumption θ is a function of time. therefore, θ can be differentiated with respect to time.
now, evaluate the second derivative at θ = 0.
d2x/dt2 = —r(dθ/dt)2
the term dθ/dt is usually called the angular velocity, which is the rate of change of the angle θ. it has units of radians/second.
for convenience we can set w ≡ dθ/dt.
d2x/dt2 = —rw2
this is the well-known form for the centripetal acceleration equation.”
no, greenhouse gases in the air, mainly carbon dioxide, methane and water vapor, trap radiation from the sun and act like a thermal blanket around the planet. without the greenhouse effect, the earth would have an average temperature of -18 °c and be covered in ice. life as we know it would not be able to survive.