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- The vibrations of a string of length L with two fixed ends 0 and L, or pressure waves that propagate along the string can be modeled by the wave equationµwtt = τwxx or µρtt = τ ρxx. Note that kinds of waves obey the same equation!The pressure waves are harder to visualize, but can be easier to visualize if you imagine the wave that travel along a slinky.(a) Find the solutions to the wave equation µwtt = τwxx with the boundaryconditions w(0) = w(L) = 0.(b) What are the possible frequencies of oscillation of the string?Which of the following conditions guarantees that two overlapping waves will exhibit the property of interference? O a. The waves must have the same frequencies. O b. The waves must be sinusoidal. O c. The waves must be coherent. O d. The waves must be in phase. O e. The waves must have the same amplitudes.In an acoustics lab you have a 120 m long pipe containing very cold air. Suppose that using a speaker you cause a sinusoidal wave of sound with frequency 150 Hz and wavelength 1.9 m to travel down the pipe. i)How long does it take for your sinusoidal wave to travel from one end of the pipe to the other end of the pipe? ii)What is the temperature of the air in the pipe?
- A water bug on the surface of a pond bobs up and down three times per second on ripples with wavelength 10.5 cm. A fish resting at the surface of the pond is 8.5 m from the water bug. How long does it take a ripple passing the water bug to reach the fish?If the sound waves produced by a speaker change to a much higher frequency, what would it sound like? O quieter O louder O lower in pitch O higher in pitcha) Show that H = Hoei(wt-kz)az Is a solution to the vector wave equation: 1 a²Ĥ = 0 c2 at2 v2 Η +
- 9. A plane seismic wave, travelling vertically downwards in a rock of density 2200 kg m-3 with seismic velocity 2000 m s-1, is incident on the horizontal top surface of a rock layer of density 2400 kg m-3 and seismic velocity 3300 m s-1. (a) What are the amplitude ratios of the transmitted and reflected waves? (b) What fraction of the energy of the incident wave is transmitted into the lower medium?#8