Recent content by Alpharup

@jim hardy...This is the first time am hearing neurophone but the concept is cool. Thanks OP.

30 W is too much, though. Some suggest that ultrasonic waves can be used to repel pests(including rats) but they also warn that higher power can damage humans too.

So, you want something like 50 Khz? If you want some mixing you can use the principles used in Amplitude modulation, where both the signals are multiplied. But, i doubt the usefulness of the method. Leaving the circuit construction aside, how can you sense ultrasonic waves? Don't we need an...

What do expect the third frequency to be?

What do you mean by the term "mixing"? does it mean voltage addition(adding function generator waveform and audio signal)?

But, can we really hear 50Khz? Is 20Khz, not the maximum frequency we can hear?

Yes, they are verily possible. We can double or triple frequency using some simple circuits. The doubled or tripled frequency signals can be used for various applications. Take the case of microprocessors. A faster clock frequency(say twice or four times) means faster operation in sequential...

Then there are something called as frequency multipliers

Do you want to increase frequency/amplitude?

Also about (i) and (ii) )

You are right. I should have posted it. Here is definition of uniform continuity.

Am fully convinced now. Thanks Stephen and Lavinia. g on [a, b] is continuous, so there is left hand continuity at b. Similarly h has Right hand continuity at b. We exploit this property. Once again, am I on right track?

I took 2 points because the definition of uniform continuity requires 2 points x and y... If (b-δ3,b+δ3) is the neighbourhood of b, there are infinitely many points k which lie in this interval. I am just taking 2 points x and y belonging to (b-δ3,b+δ3) satisfying |f(x)-f(b)|<ε/2 and...

Yes, Iam convinced of my proof but the thing is though Iam satisfied, I can't relate my modified proof with the one of Spivak. Having some experience reading the book,I feel he may skip few statements sometimes. So, I feel it is better to fit my modified proof(in the last step) with the one...