# Generation and detection of gravitational waves

### Problem 1: Mass scales

Show that effectiveness of gravitational wave production increases with the increase of mass.

### Problem 2: The intangibility

What is the reason for the very low efficiency of gravitational waves' production, i.e. conversion of mechanical energy into that of gravitational waves?

### Problem 3: Single particle effects

What happens to a single particle as a gravitational wave passes through?

### Problem 4: Waves vs static field

One may wonder, how it is possible to infer the presence of an astronomical body by the gravitational waves that it emits, when it is clearly not possible to sense its much larger stationary (essentially Newtonian) gravitational potential. What gives us hope to overcome this problem?

The next three problems are inspired by S.Hughes, Listening to the Universe with gravitational-wave astronomy, arXiv:astro-ph/0210481

### Problem 5: Listening to the Universe

What could be the origin of this poetic terminology?

### Problem 6: Measuring infinitesimal distances

The most promising sources (neutron binaries, supernovae) of gravitational waves should give the amplitudes of the order of $h\sim 10^{-21}$. For every kilometer of baseline $L$ we need to be able to measure a distance shift of $\Delta L$ better than $10^{-16}cm$. How can we possibly hope to measure an effect that is $\sim 10^{12}$ times smaller than the wavelength of visible light (all interferometers use optical lasers)?

### Problem 7: Surface effects

The atoms on the surface of the interferometers’ test mass mirrors oscillate with an amplitude $\delta l_{atom} =\sqrt{\frac{kT}{m\omega^{2}}} \sim {10}^{-10}cm$ at room temperature $T$, with $m$ the atomic mass, and with a vibrational frequency $\omega \sim {10}^{14}s^{-1}$. This amplitude is huge relative to the effect of the gravitational waves. Why doesn't it wash out the gravitational wave?