18. Waves & Sound

A satellite captures images of a tsunami, and properties of the tsunami can be found from these images, providing important information to people who need to evacuate coastal areas. If satellite images of a tsunami show the distance from one peak to another is 500 km, and the period is 1 hour, how much time do people have to evacuate if the tsunami is found to be 100 km off shore?

A wave has a wavelength of 10mm and moves at a speed of 50mm/s. What is the frequency of this wave?

(I) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed of 3.0 x 10⁸ m/s. What are the wavelengths of these signals? On FM the frequencies range from 88 MHz to 108 MHz (megahertz) and travel at the same speed. What are their wavelengths?

(I) A fisherman notices that water wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 7.5 m. How fast are the waves traveling?

I) A sound wave in air has a frequency of 265 Hz and travels with a speed of 343 m/s . How far apart are the wave crests (compressions)?

The ripples in a certain groove 10.8 cm from the center of a 33-rpm vinyl phonograph record have a wavelength of 1.55 mm. What will be the frequency of the sound emitted?

(II) The wave on a string shown in Fig. 15–35 is moving to the right with a speed of 1.10 m/s.

(b) Estimate the vertical speed of point A on the string at the instant shown in Fig. 15–35.

<IMAGE>

(II) Suppose at t= 0 , a wave shape is represented by D = A sin (2π x/ λ + ϕ) ; that is, it differs from Eq. 15–9 by a constant phase factor ϕ. What will be the equation for such a wave as a function of x and t if it travels to the left along the x axis?

When you walk with a cup of coffee (diameter 8 cm) at just the right pace of about one step per second, the coffee sloshes higher and higher in your cup until eventually it starts to spill over the top, Fig 15–41. Estimate the speed of the waves in the coffee.

<IMAGE>

(II) A 572-Hz longitudinal wave in air has a speed of 345 m/s. (a) What is the wavelength

A transverse wave pulse travels to the right along a string with a speed v = 2.4 m/s . At t = 0 the shape of the pulse is given by the function

D = 4.0m³ / (x² + 2.0m²) ,

where D and x are in meters.

(b)Determine a formula for the wave pulse at any time t assuming the pulse is traveling to the left.