Conceptual Questions

ssm Solution is in the Student Solutions Manual

| 1 | Does the principle of linear superposition imply that two sound waves, passing through the same place at the same time, always create a louder sound than either wave alone? Explain.

| 2 | Suppose you are sitting at the overlap point between the two speakers in Figure 17-4. Because of destructive interference, you hear no sound, even though both speakers are emitting identical sound waves. One of the two speakers is suddenly shut off. Describe what you would hear.

| 3 | ssm Review Figure 17-3. As you walk along a line that is perpendicular to the line between the speakers and passes through the overlap point, you do not observe the loudness to change from loud to faint to loud. However, as you walk along a line through the over lap point and parallel to the line between the speakers, you do observe the loudness to alternate between faint and loud. Explain why your observations are different in the two cases.

| 4 | At an open-air rock concert the music is played through speakers that are on the stage. The speakers point straight forward and not toward the sides. You are wandering about and notice that the sounds of the female vocalists can be heard in front of the stage but not off to the sides. The rhythmic bass, however, can be heard both in front of the stage and off to the sides. How does the phenomenon of diffraction explain your observations?

| 5 | Refer to Example 1 in 16.2. Which type of radio wave, AM or FM, diffracts more readily around a given obstacle? Give your reasoning.

| 6 | A tuning fork has a frequency of 440 Hz. The string of a violin and this tuning fork, when sounded together, produce a beat frequency of 1 Hz. From these two pieces of information alone, is it possible to determine the exact frequency of the violin string? Explain.

| 7 | ssm When the regions of constructive and destructive interference in Figure 17-15 move past a listener’s ear, a beat frequency of 2 Hz is heard. Suppose that the tuning forks in the drawing were sounded underwater and that the listener is also underwater. The forks vibrate at 438 and 440 Hz, just as they do in air. However, sound travels four times faster in water than in air. Explain why the listener hears a beat frequency of 2 Hz, just as he does in air, even though the regions of constructive and destructive interference are moving past his ear four times faster.

| 8 | The tension in a guitar string is doubled. Does the frequency of oscillation also double? If not, by what factor does the frequency change? Specify whether the change is an increase or a decrease.

| 9 | A string is attached to a wall and vibrates back and forth, as in Figure 17-18. The vibration frequency and length of the string are fixed. The tension in the string is changed, and it is observed that at certain values of the tension a standing wave pattern develops. Account for the fact that no standing waves are observed once the tension is increased beyond a certain value.

| 10 | A string is vibrating back and forth as in Figure 17-18a. The tension in the string is decreased by a factor of four, with the frequency and the length of the string remaining the same. Draw the new standing wave pattern that develops on the string. Give your reasoning.

| 11 | A rope is hanging vertically straight down. The top end is being vibrated back and forth. Standing waves can develop on the rope analogous to those on a horizontal rope. (a) There is a node at the top end. Is there a node or an antinode at the bottom end? Explain, (b) The separation between successive nodes is not the same every where on the rope, as it would be if the rope were horizontal. Is the separation greater near the top or near the bottom? Taking into account the mass of the rope, give your reasoning.

| 12 | In Figure 17-23 the tubes are filled with air. Suppose, instead, that the tube near the tuning fork labeled “Frequency = 2f” is filled with a gas in which the speed of sound is twice what it is in air. The frequency of the tuning fork remains unchanged. Draw the standing wave pattern that would exist in the tube. Justify your drawing.

| 13 | Standing waves can ruin the acoustics of a concert hall if there is excessive reflection of the sound waves that the performers generate. For example, suppose a performer generates a 2093-Hz tone. If a large-amplitude standing wave is present, it is possible for a listener to move a distance of only 4.1 cm and hear the loudness of the tone change from loud to faint. Account for this observation in terms of standing waves, pointing out why the distance is 4.1 cm.

| 14 | ssm The natural frequencies of a wind instrument change when it is brought inside from the cold outdoors. Why do the frequencies change, and is the change an increase or a decrease? Justify your answers.

| 15 | The tones produced by a typical orchestra are complex sound waves, and most have fundamental frequencies less than 5000 Hz. However, a high-quality stereo system must be able to reproduce frequencies up to 20 000 Hz accurately. Explain why.

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