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Chapter 17

Chapter 17. Sound Waves. Outline. Sound waves in general Speed of sound waves Periodic sound waves Displacement wave Pressure wave. Sound waves in general . Sound waves in air are longitudinal waves. Sound waves travel through material media .

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Chapter 17

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  1. Chapter 17 Sound Waves PHY 1371

  2. Outline • Sound waves in general • Speed of sound waves • Periodic sound waves • Displacement wave • Pressure wave PHY 1371

  3. Sound waves in general • Sound waves in air are longitudinal waves. • Sound waves travel through material media. • Speed of sound waves depend on the properties of the medium. • As the waves travel, the particles in the medium vibrate to produce changes in density and pressure. • Categories of sound waves (frequency ranges): • Audible waves: within the range of sensitivity of the human ear • Infrasonic waves: below the audible range • Ultrasonic waves: above the audible range PHY 1371

  4. Speed of sound waves • The speed of sound waves depends on the compressibility and inertia of the medium. If the medium has a bulk modulus B and density, the speed of sound waves in that medium is • The speed of all mechanical waves follows an expression of the general form • The speed of sound depends on temperature. For sound traveling through air PHY 1371

  5. Example 17.1 • (A) Find the speed of sound in water, which has a bulk modulus of 2.1 x 109 N/m2 at a temperature of 0C and a density of 1.00 x 103 kg/m3. • (B) Dolphins use sound waves to locate food. Experiments have shown that a dolphin can detect a 7.5 cm target 110 m away, even in murky water. For a bit of “dinner” at this distance, how much time passes between the moment the dolphin emits a sound pulse and the moment the dolphin hears its reflection and thereby detects the distant target? PHY 1371

  6. Periodic sound waves • Example: Sinusoidally oscillating piston. One-dimensional sinusoidal sound wave in a tube containing gas. • Compressions: Compressed regions. • Rarefactions: Low-pressure regions. • Both the compressions and rarefactions propagate along the tube with a speed equal to the speed of sound in the medium. • Any small volume of the medium moves with simple harmonic motion parallel to the direction of the wave-longitudinal wave. • The distance between two successive compressions (or rarefactions) equals the wavelength . PHY 1371

  7. Displacement wave and pressure wave • Displacement of a small element of the medium from its equilibrium position s(x,t) = smaxcos(kx - t) • smax : displacement amplitude • k: angular wave number • : angular frequency • Here, displacement s is along x – longitudinal wave. • Pressure variation P = Pmaxsin(kx - t) • Pmax = vsmax : Pressure amplitude, the maximum change in pressure from the equilibrium value. • A sound wave may be considered either as a displacement wave or a pressure wave, which are 90° out of phase with each other. PHY 1371

  8. Example: Problem #12 • As a certain sound wave travels through the air, it produces pressure variations (above and below atmospheric pressure) given by P = 1.27 sin (x – 340t) in SI units. Find • (a) the amplitude of the pressure variations, • (b) the frequency, • (c) the wavelength in air, and • (d) the speed of the sound wave. PHY 1371

  9. Homework • Ch. 17, P. 535, Problems: #2, 4, 11. • Hints: • You need to use calculus-integration for #4 (a): • First, find an expression for TC as a function of the height h above the ground; it should be linear, TC = mh + b; find the values for slope m and y-intercept b. • Second, insert the above expression for TC into the equation for sound speed v; now you have v as a function of h. • Third, time t can be calculated by setting up an integral. In this integral, replace v with the expression found in step 2. Finish the integration. PHY 1371

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