We now consider two sound waves with different frequencies which have to the same amplitude. The wave functions of these waves are as follows: y1 (t) = A sin (2πf1t) y2 (t) = A sin (2πf2t)  Find the resultant wave function analytically.  Study how the resulting wave behaves in time.

A harmonic transverse wave function is given by y(x, t) = (0.850 m) sin (15.3x + 10.4t) where all values are in the appropriate SI units. a. What are the propagation speed and direction of the waves travel? b. What are the waves period and wavelength? c. What is the amplitude? d. If the amplitude is doubled, what happens to the speed of the wave?

Two sinusoidal waves are moving through a medium in the same direction, both having amplitudes of 3.00 cm, a wavelength of 5.20 m, and a period of 6.52 s, but one has a phase shift of an angle . What is the phase shift if the resultant wave has an amplitude of 5.00 cm? [Hint: Use the trig identity sinu+sinv=2sin(u+v2)cos(uv2)

A speaker is placed at the opening of a long horizontal tube. The speaker oscillates at a frequency of f, creating a sound wave that moves down the tube. The wave moves through the tube at a speed of v=340.00 m/s. The sound wave is modeled with the wave function s(x,t)=smaxcos(kxt+) . At time t=0.00 s , an air molecule at x=2.3 m is at the maximum displacement of 6.34 nm. At the same time, another molecule at x=2.7 m has a displacement of 2.30 nm. What is the wave function of the sound wave, that is, find the wave number, angular frequency, and the initial phase shift?

A sound wave is modeled with the wave function P=1.20Pasin(kx6.28104s1t) and the sound wave travels in air at a speed of v=343.00 m/s. (a) What is the wave number of the sound wave? (b) What is the value for P(3.00 m, 20.00 s)?

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.

In figure OQ18.1 (page 566), a sound wave of wave-lenght 0.8 m divides into two equal parts that recombine to interfere constructively, with the original difference between their path lengths being |r2 r1| = 0.8 m. Rank the following situations according to the intensity of sound at the receiver from the highest to the lowest. Assume the tube walls absorb no sound energy. Give equal ranks to situations in which the intensity is equal. (a) From its original position, the sliding section is moved out by 0.1 m. (b) Next it slides out an additional 0.1 m. (c) It slides out still another 0.1 m. (d) It slides out 0.1 m more.

A sound wave traveling in air has a pressure amplitude of 0.5 Pa. What is the intensity of the wave?

As you travel down the highway in your car, an ambulance approaches you from the rear at a high speed (Fig. OQ13.15) sounding its siren at a frequency of 500 Hz. Which statement is correct? (a) You hear a frequency less than 500 Hz. (b) You hear a frequency equal to 500 Hz. (c) You hear a frequency greater than 500 Hz. (d) You hear a frequency greater than 500 Hz, whereas the ambulance driver hears a frequency lower than 500 Hz. (e) You hear a frequency less than 500 Hz, whereas the ambulance driver hears a frequency of 500 Hz. Figure OQ13.15

A wave is described by y = 0.020 0 sin (kx - t), where k = 2.11 rad/m, = 3.62 rad/s, x and y are in meters, and t is in seconds. Determine (a) (he amplitude, (b) the wavelength, (c) the frequency, and (d) the speed of the wave.