What is the physics involved with breaking glass with your voice?
Any physical object has frequencies at which they naturally vibrate, known as resonance frequencies. If we flick a crystal wine glass with finger, we will hear a fairly clear tone as the glass vibrates, causing waves of air pressure to emanate out from it, which ear and brain interpret as sound. The sound gradually gets quitter and dies out as the amplitude of the vibrations diminishes due to energy being carried away by the sound waves.
Voice is also a series of air pressure waves, with the pitch related to the frequency of the waves, and the volume related to the amplitude of the waves.
If one can match the pitch of voice to the resonant frequency of the glass the vibrating air will start the glass vibrating too. If this can be done with sufficient volume, the glass will try to move in its vibration farther and faster than the material in the glass is able to move, and the glass will break under the strain.
Why is it dangerous to look at the solar eclipse directly specially at that moment?
In general (during non-eclipse times), you've probably been told not to stare at the sun. This is because the sun simply outputs more power than our eye is designed to handle, and exposing our eye to that kind of power can damage the retina. And in a nutshell, solar eclipses are dangerous because the sun can come out from behind the moon and "surprise you" before you have a chance to look away. And this is actually even worse than when you normally look away from the sun because during the total eclipse, it is dark out, and your pupil therefore dilates so that it can let in enough light to get a good picture. Then, when the sun reappears and starts flooding the area with really bright light, not only are you staring straight at it, but your eye is in a state where it is wide open, and actively trying to let in as much light as possible.
Is a drop of water from a dropper equal in volume to a drop of mercury from the same dropper?
The size of a drop of water and a drop of mercury from the same dropper will be different. Assuming that you've filled the dropper to the same level and squeeze the dropper at the same rate, the size of the drop when it separates from the tip of the dropper and falls will be based primarily on two quantities. The first is the surface tension of the liquid and the second is the density of the liquid.
The higher the density, the more mass you have in the same sized drop.
Assuming you're doing this in a gravity environment, more mass means more weight. Which means that for the same sized drop, mercury, which has a much higher density than water, will weigh significantly more, and will therefore have more force pulling it downwards. Mercury has a density of about 13.6 g/cm3, while water has a density of 1 g/cm3.
Surface tension, in this case, provides a resistance to the downward force of gravity. Water has a much lower surface tension that mercury. Water's surface tension is about 73 dynes/cm which mercury is about 465.
So as we see, mercury is at both an advantage and a disadvantage. It has higher surface tension, which allows it to bead up more which, alone, would allow the formation of a larger drop. On the other hand, it has a higher density, which, alone, would result in a smaller drop. Which of these two factors wins out, one can't say. But the drop sizes will be different, barring a coincidence of epic proportions.
Can two persons in a plane which is traveling at a speed greater than the speed of sound will be able to hear each other?
Two people sitting in supersonic airplane such as the Concorde can easily carry out conversations, without much trouble. This is because the air is at rest inside the cabin. It is being carried forward by the airplane just as the passengers are. Since sound propagates in air, and air is at rest with respect to the speakers, everything will operate just as well as it does in any other room.
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