1.Two waves travel on the same string. Is it possible for them to have (a) different frequencies; (b) different wavelengths; (c) different speeds; (d) different amplitudes; (e) the same frequency but different wavelengths? Explain your reasoning.
2. Under a tension F, it takes 2.00 s for a pulse to travel the length of a taut wire. What tension is required (in terms of F) forthe pulse to take 6.00 s instead?
3. What kinds of energy are associated with waves on a stretched string? How could you detect such energy experimentally?
4. The amplitude of a wave decreases gradually as the wave travels down a long, stretched string. What happens to the energyof the wave when this happens?
5. For the wave motions discussed in this chapter, does the speed of propagation depend on the amplitude? What makes you say this?
6. The speed of ocean waves depends on the depth of the water; the deeper the water, the faster the wave travels. Use this toexplain why ocean waves crest and “break” as they near the shore
7. Is it possible to have a longitudinal wave on a stretched string? Why or why not? Is it possible to have a transverse Wave on a steel rod? Again, why or why not? If your answer is yes in either case, explain how you would create such a wave.
8. An echo is sound reflected from a distant object, such as a wall or a cliff. Explain how you can determine how far away theobject is by timing the echo.
9. Why do you see lightning before you hear the thunder? A familiar rule of thumb is to start counting slowly, once per second,when you see the lightning; when you hear the thunder, divide the number you have reached by 3 to obtain your distance from the lightning in kilometers (or divide by 5 to obtain your distance inmiles). Why does this work, or does it?
10. For transverse waves on a string, is the wave speed the same as the speed of any part of the string? Explain the difference between these two speeds. Which one is constant?
11. Children make toy telephones by sticking each end of a long string through a hole in the bottom of a paper cup and knotting it so it will not pull out. When the spring is pulled taut, sound can be transmitted from one cup to the other. How does this work? Why is the transmitted sound louder than the sound traveling through air for the same distance?
12. The four strings on a violin have different thicknesses, but are all under approximately the same tension. Do waves travel faster on the thick strings or the thin strings? Why? How does the fundamental vibration frequency compare for the thick versus the thin strings?
13. A sinusoidal wave can be described by a cosine function, which is negative just as often as positive. So why isn’t the averagepower delivered by this wave zero?