Download Physics Problem Set 11: Waves and Their Properties and more Assignments Physics in PDF only on Docsity! Physics 2010 (Schroeder) Name spring 2004 Problem Set 11 (due Monday, April 5) 1. A periodic wave on a long, taut cord has a speed of 240 m/s and a wavelength of 3.2 m. What are the (a) frequency and (b) period of this wave? 2. Ocean waves in a certain location have a wavelength of 40 meters, an amplitude of 1.5 meters, and a period of 5 seconds. (a) What is the (horizontal) speed of the waves? (b) A duck is floating on the water as these waves pass by. Very roughly, what is the average speed of the duck’s motion? 3. The speed of electromagnetic waves in vacuum is 3.0 × 108 m/s. (a) Wavelengths of visible light waves range from about 400 nm (violet) to about 700 nm (red). What is the range of frequencies of visible light waves? (b) The range of frequencies for shortwave radio (including FM and VHF television) is 1.5 MHz to 300 MHz. What is the corresponding wavelength range? (c) X-rays are also electromagnetic waves. Their wavelength range extends from about 5.0 nm to about 0.01 nm. What is the corresponding frequency range? 4. Suppose you are wiggling the end of a long string, to produce a sinusoidal wave. After a while, you double the frequency of your wiggles, without changing the string tension. (a) What happens to the speed of the waves produced? (b) What happens to the wavelength of the waves produced? 5. The speed of a transverse wave on a string is 170 m/s when the string tension is 120 N. To what value must the tension be changed to raise the wave speed to 180 m/s? 6. Two pulses travel along a string in opposite directions, as shown below. (a) If the wave speed is 2.0 m/s and the peaks of the pulses are 6.0 cm apart at t = 0, sketch the patterns when t = 5, 10, 15, 20, and 25 milliseconds. (b) What has happened to the energy of the pulses at t = 15 ms? 7. Two identical sinusoidal traveling waves, moving in the same direction, are out of phase by π/2 radians. These waves combine to form a single resultant wave. How does the amplitude of the resultant wave compare to the amplitudes of the original waves? (Please answer this question by carefully plotting both waves, then adding the waves graphically and measuring the resulting amplitude with a ruler.) 8. A nylon guitar string has a length of 90 cm (between the fixed supports), a tension of 150 N, and a mass per unit length of 7.2 g/m. (a) What is the speed of traveling waves on this string? (b) Suppose that the string is oscillating in a standing wave pattern with two nodes (hence three “bumps”). What is the wavelength of this standing wave? (c) What is the frequency of the standing wave? 9. A 1.5 meter wire has a mass of 8.7 g and is held under a tension of 120 N. The wire is held from both ends and set into vibration. Calculate (a) the speed of waves on the wire; (b) the
