7. If wavelength of third harmonic of standing waves in a sting is 5m, what is the length of the string? Ch. 16 Problems ( each, Due 9/15) 1. A guitar is tuned when the tension in its strings is adjusted. Should you increase or decrease the tension in a string to produce a higher-frequency 8. A piano tuner simultaneously strikes a 262 Hz tuning fork and the middle C key on a piano and hears beats with a beat period of 0.500 s. What are the possible frequencies of the slightly out-of-tune key? Should the tension in the piano wire be changed in such a way as to shorten or to lengthen the period of the beats? sound? 2. A cork floating on a lake bobs up and down as a small wave passes. The cork completes 4.00 cycles in 1.00 s. The wave peaks are 10.0 cm apart. Find the speed of the wave 3. A wave traveling in the positive x-direction has a frequency of 25.0 Hz, as in Figure P13.37. Find the (a) amplitude, (b) wavelength, (c) period, and (d) speed of the wave. 9. A pipe closed at one of its ends has a length 18.0 cm of 0.8m. What is the distance between a node and adjacent anti-node of its second harmonic. 10. The longest pipe in a certain organ is 4.00 m long. What is the lowest frequency the organ will produce if the pipe is (a) open at both ends; (b) closed at one end? 10.0 cm 4. A 1.00 m long string of mass 0.0100 kg, under a tension of 100 N, transmits a wave of amplitude 2.00 cm and wavelength 10.0 cm. (a) Find the speed of the wave form. (b) How far does a particle of the string travel during one cycle? (c) What is the average speed of a particle of the string? 5. In the arrangement shown, an object can be hung from a string (with linear mass density u =0.002 00 kg/m) that passes over a light pulley. The string is connected to a vibrator (of constant frequency f), and the length of the string between point P and the pulley is L = 2.00 m. When the mass m of the object is either 16.0 kg or 25.0 kg, standing waves are observed; however, no standing waves are observed with any mass between these values. (a) What is the frequency of the vibrator? (b) What is the largest object mass for which standing waves could be observed? Extra (might be on test - don't hand in) 11. If a long rope is hung from a ceiling and waves are sent up the rope from its lower end, they do not ascend with constant speed. Explain. 12. An airplane mechanic notices that the sound from a twin-engine aircraft rapidly varies in loudness when both engines are running. What could be causing this variation from loud to soft? 13. If one end of a heavy rope is attached to one end of a light rope, the speed of a wave will change as the wave goes from the heavy rope to the light one. Will the speed increase or decrease? What happens to the frequency? To the wavelength? Vibrator L- P 14. Find the speed of sound in mercury, which has a bulk modulus of approximately 2.80 x 1010 N/m? and a density of 13 600 kg/m³. 6. A sound source moves through air toward a stationary observer. The frequency of the sound the observer hears is 20.0% higher than the source frequency. How fast is the source moving? 15. A 60.000-cm guitar string under a tension of 50.000 N has a mass per unit length of 0.100 00 g/cm. What is the highest resonant frequency that can be heard by a person capable of hearing frequencies up to 20 000 Hz?