18. Waves & Sound

A sound wave is emitted at a frequency of 300 Hz in air at a 0°C. As the sound wave travels through the air, the temperature increases. What is the wavelength of the sound wave at the following temperatures?

a. 0°C
b. 20°C
c. 45°C

A metal bar $$has a length of 1.5 m and a density of 6400 kg/m³. Sound waves take 3.9 × 10^-4 s to travel along the length of the bar. What is Young's modulus for this metal?

(I) Calculate the speed of longitudinal waves in

(b) granite, using Tables in Chapters 12 and 13.

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(II) A sailor strikes the side of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 2.4 s later. How deep is the ocean at this point? (Use Tables 12–1 and 13–1.)

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Two solid rods have the same bulk modulus but one is 2.1 times as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what factor?

A motion sensor can accurately measure the distance d to an object repeatedly via the sonar technique used in Example 16–2. A short ultrasonic pulse is emitted and reflects from any objects it encounters, creating echo pulses upon their arrival back at the sensor. The sensor measures the time interval t between the emission of the original pulse and the arrival of the first echo.

(b) To measure an object’s speed the motion sensor makes 15 distance measurements every second (that is, it emits 15 sound pulses per second at evenly spaced time intervals), the measurement of t must be completed within the time interval between the emissions of successive pulses. What is the largest distance (at 20°C) that can be measured with the motion sensor?

(II) P and S waves from an earthquake travel at different speeds, and this difference helps locate the earthquake “epicenter” (where the slippage took place).

(a) Assuming typical speeds of 8.5 km/s and 5.5 km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 1.5 min apart?

(II) Determine the wavelength of a 6200-Hz longitudinal wave traveling along an iron rod. Use Tables 12–1 and 13–1.

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