Water waves in the sea are observed to have a wavelength of 300 m and a frequency of 0.07 Hz. The velocity of these waves is: 0.00021 m/s O 2.1 m/s 21 m/s 210 m/s
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- A sound wave in air has a pressure amplitude equal to 4.00 103 Pa. Calculate the displacement amplitude of the wave at a frequency of 10.0 kHz.During a thunderstorm, a frightened child is soothed by learning to estimate the distance to a lightning strike by counting the time between seeing the lightning and hearing the thunder (Fig. P2.25). The speed vs of sound in air depends on the air temperature, but assume the value is 343 m/s. The speed of light c is 3.00 108 m/s. a. A child sees the lightning and then counts to eight slowly before hearing the thunder. Assume the light travel time is negligible. Estimate the distance to the lightning strike. b. Using your estimate in part (a), find the light travel time. Is it fair to neglect the light travel time? c. Think about how time was measured in this problem. Is it fair to neglect the difference between the speed of sound in cold air (vs at 0C = 331.4 m/s) and the speed of sound in very warm air (vs at 40C = 355.4 m/s)?Submarine A travels horizontally at 11.0 m/s through ocean water. It emits a sonar signal of frequency f = 5.27 103 Hz in the forward direction. Submarine B is in front of submarine A and traveling at 3.00 m/s relative to the water in the same direction as submarine A. A crewman in submarine B uses his equipment to detect the sound waves (pings) from submarine A. We wish to determine what is heard by the crewman in submarine B. (a) An observer on which submarine detects a frequency f as described by Equation 16.46? (b) In Equation 16.46, should the sign of vs be positive or negative? (c) In Equation 16.46, should the sign of vo be positive or negative? (d) In Equation 16.46, what speed of sound should be used? (e) Find the frequency of the sound detected by the crewman on submarine B.
- A sound wave traveling in air has a pressure amplitude of 0.5 Pa. What is the intensity of the wave?Earthquakes at fault lines in the Earths crust create seismic waves, which are longitudinal (P waves) or transverse (S waves). The P waves have a speed of about 7 km/s. Estimate the average bulk modulus of the Earths crust given that the density of rock is about 2 500 kg/m3.A yellow submarine traveling horizontally at 11.0 m/s uses sonar with a frequency of 5.27 103 Hz. A red submarine is in front of the yellow submarine and moving 3.00 m/s relative to the water in the same direction. A crewman in the red submarine observes sound waves (pings) from the yellow submarine. Take the speed of sound in seawater as 1 533 m/s. (a) Write Equation 14.12. (b) Which submarine is the source of the sound? (c) Which submarine carries the observer? (d) Does the motion of the observers submarine increase or decrease the time between the pressure maxima of the incoming sound waves? How does that affect the observed period? The observed frequency? (e) Should the sign of v0 be positive or negative? (f) Does the motion of the source submarine increase or decrease the time observed between the pressure maxima? How does this motion affect the observed period? The observed frequency? (g) What sign should be chosen for vs? (h) Substitute the appropriate numbers and obtain the frequency observed by the crewman on the red submarine.
- Rank the waves represented by the following functions from the largest to the smallest according to (i) their amplitudes, (ii) their wavelengths, (iii) their frequencies, (iv) their periods, and (v) their speeds. If the values of a quantity are equal for two waves, show them as having equal rank. For all functions, x and y are in meters and t is in seconds. (a) y = 4 sin (3x 15t) (b) y = 6 cos (3x + 15t 2) (c) y = 8 sin (2x + 15t) (d) y = 8 cos (4x + 20t) (e) y = 7 sin (6x + 24t)Show that an intensity of 1012 W/m2 is the same as 1016 W/cm2.A sound wave can be characterized as (a) a transverse wave, (b) a longitudinal wave, (c) a transverse wave or a longitudinal wave, depending on the nature of its source, (d) one that carries no energy, or (e) a wave that does not require a medium to be transmitted from one place to the other.
- Problems 32 and 33 are paired. N Seismic waves travel outward from the epicenter of an earthquake. A single earthquake produces both longitudinal seismic waves known as P waves and transverse waves known as S waves. Both transverse and longitudinal waves can travel through solids such as rock. Longitudinal waves can travel through fluids, whereas transverse waves can only be sustained near the surface of a fluid, not inside the fluid. When seismic waves encounter a fluid medium such as the liquid outer core of the Earth, only the longitudinal P wave can propagate through. Geophysicists can model the interior of the Earth by knowing where and when S and P waves were detected by seismographs after an earthquake (Fig. P17.32). Assume the average speed of an S wave through the Earths mantle is 5.4 km/s and the average speed of a P wave is 9.3 km/s. After an earthquake, a seismograph finds that the P wave arrives 1.5 min before the S wave. How far is the epicenter from the detector? FIGURE P17.32The equation of a harmonic wave propagating along a stretched string is represented by y(x, t) = 4.0 sin (1.5x 45t), where x and y are in meters and the time t is in seconds. a. In what direction is the wave propagating? be. N What are the b. amplitude, c. wavelength, d. frequency, and e. propagation speed of the wave?A siren mounted 011 the roof of a firehouse emits sound at a frequency of 900 Hz. A steady wind is blowing with a speed of 15.0 m/s. Taking the speed of sound in calm air to be 343 m/s. find the wavelength of the sound (a) upwind of the siren and (b) downwind of the siren. Firefighters are approaching the siren from various directions at 15.0 m/s. What frequency does a firefighter hear (c) if she is approaching from an upwind position so that site is moving in the direction in which the wind is blowing and (d) if she is approaching from a downwind position and moving against the wind?