Q & A (Integral of Root Sin x)

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When the Doorbell Rings @ 4 AM......

8th July 2007

Initially, I thought to put this post this on another blog but later I thought that it had something to with Physics and decided to put it here.

At around 4 AM in the night amidst heavy rains if the doorbell rings then one can get suspicious at first. And if after checking one finds that there is no one at the door then it may be a feeling of relief with curiosity. I had this experience and since I was aware of such incident (doorbell ringing on its own), I was keen to investigate what could have caused this in my case. My doorbell was not wireless which could be triggered by the switch of my neighbour (if coincidentally both doorbells worked at same frequency). The bell I use is a musical bell connected to the switch via wires.

The bell under consideration plays music only once at the time of pressing the switch. If one continues to press the switch it won't keep on playing music. On the day the doorbell played music at 4 AM, it did not do so later even if someone pressed the switch. However, when the mains power was switched off and switched on again, the doorbell did play music. Now, it looked as if at 4 AM something caused the two wires in the switch to come in electrical contact. When it happened first (i.e. at 4 AM on that day), there was music. Subsequently, since the wires remained in electrical contact, pressing the switch was irrelevant and doing so did not cause it to play music. When the mains was switched off, now even though those two wires remained in electrical contact, there was disconnection in the circuit and it played music when the mains was switched on.

While all these experiments confirm the theory that at 4 AM on that particular day, the two wires did come into contact, one can still wonder what could have caused them to come in contact. Was it wind? But then inside the switch where two wires are there, the effect of wind should be subdued. Since switch is outside, it could be the rain causing the two points to come in electrical contact (it doesn't necessarily have to be a physical contact). The water can find its way through a switch which is not water tight.

5th May 2008

I have been thinking about updating this post since a past few months. The bell rang later after rainy season when there were no rains. I tried to see inside the switch to investigate what could be responsible for the electrical contact and I could find a wasp there.

IIT JEE 2008 Paper I Maths Calculus Write Up

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Sound Waves

Here are some additional points which may be useful besides the standard discussion of Doppler's Effect.

1. If listener is moving towards the source (irrespective of source moving towards, away or remaining stationary) then the listener is able to get the waves more quickly. In this case the speed of sound for the listener is more. For example in a write-up based question in JEE 2007*, the engine of train A was blowing whistle and the speed of sound for the passenger of the same train would be 340+20=360 m/s.
2. If listener is moving away from the source (irrespective of the source moving towards, away or remaining stationary) then the listener is able to get the waves with some delay (it is as if the listener is running away from them). In this case the speed of sound for the listener is less. For example in a write-up based question in JEE 2007*, the engine of train A was blowing whistle and the speed of sound for the passenger of train B moving in front would be 340-30=310 m/s.
3. When source is moving towards or away from the listener (irrespective of the motion of the listener) then the wavelength changes. If source is not moving wavelength does not change. This is because if the source is moving (say) towards the listener, then the distance between the two consecutive wavefronts would be smaller (second wavefront leaves the source when it already have moved forward). If the source is moving away from the listener, then the distance between the two consecutive wavefronts would be more (second wavefront leaves the source when the source has moved backward).

*Two trains A and B are moving with speeds 20 m/s and 30 m/s respectively in the same direction on the same straight track with B ahead of A. The engines are at the front ends. The engine of train A blows a long whistle. The speed of sound in still air is 340 m/s.

Atomic Structure

A spectroscopic instrument can resolve two nearby wavelengths and if is smaller than 8,000. This is used to study the spectral lines of the Balmer series of hydrogen. Approximately how many lines will be resolved by the instrument?