THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

68 3. Sound Wave Propagation and CharacteristicsProblems for Chapter 31. A signal consists of the following components:y 1 = 10 sin 4t, y 2 = 6 sin 8t, y 3 = 4.3 sin 10tPlot each component and add them up to obtain a composite wave.2. A 300-Hz sound wave is propagating axially in a steel bar. Find the wavelengthand the wave number.3. Determine the wave number and the wavelength of a 30-Hz pure tone at20 ◦ C.4. Two sine waves have approximately the same amplitudes, but one is at afrequency of 135.3 Hz and the other 136.0 Hz. What is the beat frequency?What is the time duration between the beats?5. Show mathematically how noise cancellation can be effected by duplicatingan offending signal and changing its phasing. In real life situation, can thecancellation be a total one? If not, why not?6. It is desired to place a worker at a “quieter” location near a machine that putsout a steady 400 Hz hum. Where would this location be and where are thepoints where the noise would be greater?7. A train whistle is measured with its frequency at 250 Hz when the trainsapproaches the observer near the tracks at the rate of 125 km/h. Predict thefrequency when the train is pulling away from the observer.8. Train A traveling 60 km/h is approaching Train B traveling on a parallel trackat 85 km/h. Train A blows its whistle which has a fundamental of 255 Hz. Whatfrequency will the engine man at Train B hear? What will be the perceivedfrequency after the whistle on Train B passes the locomotive of Train A?Neglect the distance between the tracks.9. An observer stands 150 km from a railroad track. A train is 300 km on thenormal from the track to the observer. It is traveling at 80 km/h and approachingthis normal. Its whistle emits a fundamental of 300 Hz. What will be thefrequency of this signal perceived by the observer?10. Develop an equation for the rate of change of the frequency with respect toan observer subtending an angle θ with a source’s direction. The source ismoving at a velocity V .11. A boundary exists between two mediums, A and B, through which an acousticsignal travels. The signal traveling in Medium A impinges the boundary atan angle of 45 ◦ . In passing into Medium B on the other side of the boundarythe signal refracts at an angle of 55 ◦ . The velocity of sound in Medium A is450 m/s. Determine the velocity of sound in Medium B on the other side ofthe boundary.12. Given a 150-Hz signal expressed asp(x, t) = 35 sin 2.5(x − 344t)determine the followings: