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After a point the extra frequency doesn't help. However I have a high speed video of my toxic hard bat being hit by a TT ball. It is clear the ball pushes or deforms the blade and the ball bounces back before the toxic 5 blade can rebound to help push the ball back. All the energy the ball imparts on the blade is lost.
What needs to happen for optimal speed is for the ball to push the toxic 5 back then the toxic 5 pushes the ball back. This means that some of the energy on the toxic 5 is being returned to the ball as it pushes the ball back. Once the ball leaves the paddle, any vibration in the paddle is lost energy.
The toxic 5 blade has a very low frequency of vibration and is very slow and discontinued
This is a too slow example.
An important thing to remember is that any motion/vibration in the paddle after the ball leaves the rubber is wasted energy.
So what if the paddle has a frequency of 1000 Hz?
In this case a complete cycle is 1 millisecond = 0.001 second.
A half cycle where the paddle is deformed and springs back is 1/2 a millisecond.
This would be optimal if the contact time is also 1/2 millisecond because the blade would be pushed back by the ball for the first quarter millisecond and then the blade would push the ball back during most of the second quarter of a millisecond. The longer the blade can keep the rubber in contact with the ball the more energy it can return to the ball.
So why not have very stiff blades with very high frequencies?
The problem here is that the ball only impacts with so much energy. Some is absorbed by the ball, some by the rubber and a little by the blade. However very stiff high frequency blades will have very low amplitudes of vibration because the energy in the blade is proportional the Amp((2*PI*Hz)^2 so the amplitude decreases very quickly as the frequency increases. If the amplitude is small, the blade will not be able to push the ball on the rebound if at all.
In short, there is such a thing as blades with too low a frequency and too high. Blades with frequencies over 1000 Hz are not going to be much different from each other because they don't push the ball back in phase with the ball and rubber decompressing and the amplitudes of vibration will be too small.
What needs to happen for optimal speed is for the ball to push the toxic 5 back then the toxic 5 pushes the ball back. This means that some of the energy on the toxic 5 is being returned to the ball as it pushes the ball back. Once the ball leaves the paddle, any vibration in the paddle is lost energy.
The toxic 5 blade has a very low frequency of vibration and is very slow and discontinued
This is a too slow example.
An important thing to remember is that any motion/vibration in the paddle after the ball leaves the rubber is wasted energy.
So what if the paddle has a frequency of 1000 Hz?
In this case a complete cycle is 1 millisecond = 0.001 second.
A half cycle where the paddle is deformed and springs back is 1/2 a millisecond.
This would be optimal if the contact time is also 1/2 millisecond because the blade would be pushed back by the ball for the first quarter millisecond and then the blade would push the ball back during most of the second quarter of a millisecond. The longer the blade can keep the rubber in contact with the ball the more energy it can return to the ball.
So why not have very stiff blades with very high frequencies?
The problem here is that the ball only impacts with so much energy. Some is absorbed by the ball, some by the rubber and a little by the blade. However very stiff high frequency blades will have very low amplitudes of vibration because the energy in the blade is proportional the Amp((2*PI*Hz)^2 so the amplitude decreases very quickly as the frequency increases. If the amplitude is small, the blade will not be able to push the ball on the rebound if at all.
In short, there is such a thing as blades with too low a frequency and too high. Blades with frequencies over 1000 Hz are not going to be much different from each other because they don't push the ball back in phase with the ball and rubber decompressing and the amplitudes of vibration will be too small.