Dr. Jie ZouPHY Chapter 17 Sound Waves

Dr. Jie ZouPHY Outline Sound waves in general Speed of sound waves Periodic sound waves Displacement wave Pressure wave

Dr. Jie ZouPHY 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

Dr. Jie ZouPHY 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

Dr. Jie ZouPHY Example 17.1 (A) Find the speed of sound in water, which has a bulk modulus of 2.1 x 10 9 N/m 2 at a temperature of 0  C and a density of 1.00 x 10 3 kg/m 3. (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?

Dr. Jie ZouPHY 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.

Dr. Jie ZouPHY Displacement wave and pressure wave Displacement of a small element of the medium from its equilibrium position s(x,t) = s max cos(kx -  t) s max : displacement amplitude k: angular wave number  : angular frequency Here, displacement s is along x – longitudinal wave. Pressure variation  P =  P max sin(kx -  t)  P max =  v  s max : 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.

Dr. Jie ZouPHY 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.

Dr. Jie ZouPHY Homework Ch. 17, P. 535, Problems: #2, 4, 11. Hints: You need to use calculus-integration for #4 (a): First, find an expression for T C as a function of the height h above the ground; it should be linear, T C = mh + b; find the values for slope m and y-intercept b. Second, insert the above expression for T C 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.