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Chapter 14: Problem 4
If you doubled the tension in a string, what would happen to the speed of waves on the string?
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The intensity of light from a localized source decrenses as the inverse square of the distance from the source. Does this mean that the light loses energy as it propagates?
A star is orbiting the galactic center, and at a point in its orbit when it's heading in the direction toward Earth, it's moving at \(64.8 \mathrm{~km} / \mathrm{s}\). An astronomer observes a spectral line emitted by hydrogen atoms in the star's atmosphere; the wavelength relative to the emitting atoms is \(656.28 \mathrm{~nm}\). By how much will the astronomer observe this wavelength to be shifted?
Find the sound speed in air under standard conditions with pressure \(101 \mathrm{kN} / \mathrm{m}^{2}\) and density \(1.20 \mathrm{~kg} / \mathrm{m}^{3}\).
Gravitational waves were first detected in 2015, using the LIGO detectors at Livingston, Louisiana, and Hanford, Washington. The gravitational waves, propagating as plane waves, reached the Livingston detector \(7.0 \mathrm{~ms}\) before they reached Hanford. (a) Did the waves come from the southern or northern hemisphere of the sky? (b) Estimate the straight-line distance between Livingston and Hanford and, using the fact that gravitational waves propagate at the speed of light, find the approximate angle between the direction of the waves' propagation and the Livingston-Hanford line. Knowing this angle helped LIGO scientists to determine an upproximate location of the source.
Two waves have the same angular frequency \(\omega\), wave number \(k\), and amplitude \(A\), but they differ in phase: \(y_{1}=A \cos (k x-\omega t)\) and \(y_{2}=A \cos (k x-\omega t+\phi)\). Show that their superposition is also a simple harmonic wave, and determine its amplitude as a function of the phase difference \(b\).
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