What are the three longest wavelengths for standing sound waves in a 121-cm long tube that is open at both ends? Draw pictures of each of these situations and calculate their wavelengths.
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- 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) If a submarine’s sonar can measure echo times with a precision of 0.00100 s, what is the smallest difference in distances it can detect? (Assume that the submarine is in the ocean, not in fresh water.) (b) Discuss the limits this time resolution imposes on the ability of the sonar system to detect the size and Shape of the object creating the echo.Many of the topics discussed in this chapter are useful beyond the topics of mechanical waves. It is hard to conceive of a mechanical wave with sharp corners, but you could encounter such a wave form in your digital electronics class, as shown below. This could be a signal from a device known as an analog to digital converter, in which a continuous voltage signal is converted into a discrete signal or a digital recording of sound. What is the result of the superposition of the two signals?
- Two sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string producing a standing wave. The linear mass density of the string is =0.075 kg/m and the tension in the string is FT=5.00 N. The time interval between instances of total destructive interference is t=0.13 s. What is the wavelength of the waves?(a) If a submarine’s sonar can measure echo times with a precision of 0.0100 s, what is the smallest difference in distances it can detect? (Assume that the submarine is in the ocean, not in fresh water.) (b) Discuss the limits this time resolution imposes on the ability of the sonar system to detect the size and shape of the object creating the echo.Six members of a synchronized swim team wear earplugs to protect themselves against water pressure at depths, but they can still hear the music and perform the combinations in the water perfectly. One day, they were asked to leave the pool so the dive team could practice a few dives, and they tried to practice on a mat, but seemed to have a lot more difficulty. Why might this be?
- (a) What is the speed of sound in a medium where a 100-kHz frequency produces a 5.96-cm wavelength? (b) Which substance in Table 17.1 is this likely to be?(a) Find the size of the smallest detail observable in human tissue with 20.0-MHz ultrasound. (b) Is its effective penetration depth great enough to examine the entire eye (about 3.00 cm is needed)? (c) What is the wavelength of such ultrasound in 0°C air?(a) Ear trumpets were never very common, but they did aid people with hearing losses by gathering sound over a large area and concentrating it on the smaller area of the eardrum. What decibel increase does an ear trumpet produce it its sound gathering area is 900 cm2 and the area of the eardrum is 0.500 cm2, but the trumpet only has an eficiency of 5.00% in transmitting the sound to the eardrum? (b) Comment on the usefulness of the decibel increase found in part (a).
- The speaker system at an open-air rock concert forms a ring around the entire circular stage and delivers 50,000 W of power output. Assume the sound radiates in all directions equally as if it were generated by an isotropic point source and assume the sound energy is not absorbed by air. a. At what distance is the sound from the speakers barely audible? Note that your answer will be far too large since the model we are using for sound level ignores the power absorbed by the medium (air). How does your answer compare to the radius of the Earth? b. What is the closest distance audience members can be to the speakers if the sound is not to be painful to their ears?You are working at an open-air amphitheater, where rock concerts occur regularly. The venue has powerful loudspeakers mounted on 10.6-m-tall columns at various locations surrounding the audience. The loudspeakers emit sound uniformly in all directions. There are ladder steps sticking out from the columns, to help workers service the loudspeakers. Many times, audience members break through the protective fencing around the columns and climb upward on the columns to get a better view of the performers. The upcoming concert is by a group that states that several very-high-volume pulses of sound occur in their concerts, and these sounds are part of their artistic expression. The amphitheater owners are worried about people climbing the columns and being too close to the loudspeakers when these peak sounds are emitted. They do not want to be held responsible for injuries to audience members ears. Based on past performances of the group, you determine that the peak sound level is 150 dB measured 20.0 cm from the speakers on the columns. The owners ask you to determine the heights on the columns at which to mount impassable barricades to keep people from getting too close to the speakers and hearing sound above the threshold of pain.A barrel organ is shown in Figure P18.38. Such organs are much smaller than traditional organs, allowing them to fit in smaller spaces and even allowing them to be portable. Use the photo to estimate the range in fundamental frequencies produced by the organ pipes in such an instrument. Assume the pipes are open at both ends. How does that range compare to a piano whose strings range in fundamental frequency from 21.7 Hz to 4186.0 Hz? FIGURE P18.38