#8#14#22#26#34#40#42#48#52#54#588. When the time interval between seeing the lightning and hearing the thunder is short, the thunder is loud. Why?
The time interval between seeing the lightning and hearing the thunder indicates the distance to the storm since the sound of thunder travels about a mile through air in five seconds. When this time is short, the storm must be nearby. The sound that we hear is a portion of the sound energy leaving the area of the lightning and traveling out in all directions. The closer we are to the source of the sound, the less the sound energy has dispersed during its travel and the louder the thunder will be.
14. What property of a sound wave determines its loudness (or intensity)?
A sound wave can be accurately described by specifying its environment (air, water, etc.) direction of travel, wavelength (or frequency), and amplitude. Of these, only the amplitude (when squared) specifies the intensity, or loudness, of the wave.
22. How can you change the speed of the waves on a guitar string?
When we looked at the natural vibration frequency of a mass on a spring, we said that the frequency increased as the spring became stiffer. For the guitar string, this would be the same as increasing the tension on the string. Since the speed of a wave is equal to its wavelength times its frequency, and the fundamental wavelength is determined by the length of the string, the speed of the wave will increase when the tension in the guitar string increases.
26. Where on a guitar sring of length L would you place your finger to damp out the third harmonic? Do these places differ in their effect on other harmonics?
You can damp out a specific harmonic by putting your finger at a point where it has an anti-node, a location of maximum amplitude, to change it into a node location. The third harmonic has two nodes along the length of the string located at a distance of L/3 from either end. It has anti-nodes at a distance of L/6 from either end, and at the midpoint (L/2). Placing your finger at the midpoint anti-node will damp out all odd harmonics (first, third, fifth, ...) as they all have anti-nodes at this location, but it will not effect the even harmonics (second, fourth, ...) which have a node at the midpoint. Placing your finger at either of the L/6 anti-nodes will effect most of the harmonics (even and odd) as nearly all have some wave amplitude at this location.
34. How long is the wavelength of the fundamental in an open organ pipe compared with the length of the pipe?
An open organ pipe has both ends open. Recalling that an open (or free) end requires an anti-node in a standing wave, the open organ pipe has an anti-node at both ends of the pipe. However, there must be a node between a pair of consecutive anti-nodes. So, the fundamental of the open pipe has anti-nodes at each end and a node at the midpoint. This corresponds to one-half of a wavelength, so the wavelength of the fundamental is twice the length of the pipe.
40. What happens to the frequency of an organ pipe if you saw off a bit of the end of the pipe?
Suppose that we saw a section off of the open end of an organ pipe. This shortened pipe now determines the length of the fundamental wavelength, which is also shorter! Recalling that the speed of sound is unchanged, and that the wavelength times the frequency is equal to the speed of sound, we see that the frequency increases because the wavelength has decreased.
42. What would happen to the frequency of an organ pipe if it were filled with helium instead of air?
The fundamental wavelength of the organ pipe is determined by its length, so this wavelength stays the same. Since the speed of sound in helium is greater than the speed of sound in air, and the wavelength times the frequency equals the speed of sound, the frequency is greater in the organ pipe filled with helium.
48. As the frequencies of two waves get closer together, what happens to the beat frequency?
Recall that the beat frequency is equal to the difference between the two wave frequencies. As the frequencies of the two waves get closer together, the beat frequency gets smaller.
52. Would you expect to hear a lower, the same, or a higher frequency as a tuning fork moves away from you? Explain your reasoning.
You would expect to hear a lower frequency because of the Doppler effect. The tuning fork vibrates at the same frequency whether it is moving or stationary. The sound waves leave the tuning fork with the same separation in time according to the tuning fork, because they are produced by the vibration of the tuning fork. But when the tuning fork is moving away from you, its motion increases the distance between successive wavefronts by an amount equal to its speed times the period of the tuning fork. (This is our friend, the distance equation, again.) Since the speed of sound in air remains the same while the wavelength has increased, the frequency you hear must decrease.
54. Which of the following properties of the wave does not change in the Doppler effect: wavelength, speed, or frequency?
The speed of sound does not depend on the motion of the source of the sound, only on the material carrying the sound. The frequency and wavelength change together, yielding this constant value of wave speed.
58. When does a sonic boom occur?
A shock wave is produced when an object emitting sound is moving through air (or other medium) at a speed equal to or greater than the speed of sound. The shock wave is located at the region where the outgoing sound waves (from our rapidly moving source) line up and overlap, increasing the sound intensity in a region. (This overlap of sound waves, or later sound waves catching up with earlier ones, is possible only because our sound source is traveling faster than the already emitted sound waves.) When the traveling shock wave passes by your location, we call what you hear a sonic boom.