Part I. Open Open Pipes. A 35 cm long string is played at its fundamental frequency.
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1 Part I Open Open Pipes A 35 cm long pipe is played at its fundamental frequency. 1. What does the waveform look like inside the pipe? 2. What is this frequency s wavelength? 3. What is this frequency being played if the speed of sound is 345 m/sec? A 35 cm long pipe is played at its 1 st overtone, or second harmonic. 4. What does the waveform look like inside the pipe? 5. What is this frequency s wavelength? 6. What is this frequency being played if the speed of sound is 345 m/sec? Open Closed Pipes A 35 cm long pipe is played at its fundamental frequency. 1. What does the waveform look like inside the pipe? 2. What is this frequency s wavelength? 3. What is this frequency being played if the speed of sound is 345 m/sec? A 35 cm long pipe is played at its 1 st overtone, or third harmonic. 4. What does the waveform look like inside the pipe? 5. What is this frequency s wavelength? 6. What is this frequency being played if the speed of sound is 345 m/sec? Fixed Fixed Strings A 35 cm long string is played at its fundamental frequency. 1. What does the waveform look like along the string? 2. What is this frequency s wavelength? 3. What is this frequency being played if the wave speed is 345 m/sec? A 35 cm long string is played at its 1 st overtone, or second harmonic. 4. What does the waveform look like along the string? 5. What is this frequency s wavelength? 6. What is this frequency being played if the wave speed is 345 m/sec? Which case has the highest fundamental frequency? Open Open pipe Open Closed pipe Fixed Fixed String
2 Part II What is the wavelength of each standing wave in the following cases? In each diagram, the solid line is the original wave and the dashed line is its reflection. The length of the string is 45 cm. The length of the pipe is 20 cm. Which type of pipe is it? open open or open closed? The length of the pipe is 30 cm. Which type of pipe is it? open open or open closed? The length of the string is 40 cm.
3 The length of the pipe is 70 cm. Which type of pipe is it? open open or open closed? The length of the pipe is 45 cm. Which type of pipe is it? open open or open closed? Part III What length of open closed PVC pipe would resonant at a fundamental frequency of 256 hz if the speed of sound was 345 m/sec? What length of open closed PVC pipe would resonant at a fundamental frequency of 512 hz if the speed of sound was 345 m/sec?
4 The data shown above in yellow (B6 through B11 and F6 through F11) )was obtained in a speed of sound lab. Make sure that you understand HOW each numerical value in columns D (wavelength) and H (period) were calculated. Write the equation of their line of best fit using the correct variables. What property of sound does the slope of their line of best fit represent? The equation for the speed of sound traveling through dry air is v w = T, where T is the temperature measured in degrees Celsius. Verify that the speed of sound in cell C21 is correct. Is the percent difference (cell C18) correctly calculated? Show your calculation below.
5 Part IV A vibrating tuning fork is held above a column of air, as shown in the diagrams above. The reservoir is raised and lowered to change the water level, and thus the length of the column of air. The shortest length of air column that produces a resonance is L 1 = 0.25 m, and the next resonance is heard when the air column is L 2 = 0.80 m long. The speed of sound in air at 20 C is 343 m/sec and the speed of sound in water is 1490 m/sec. (a) Calculate the wavelength of the standing sound wave produced by this tuning fork. (b) Calculate the frequency of the tuning fork that produces the standing wave, assuming the air is at 20 C (c) Calculate the wavelength of the sound waves produced by this tuning fork in the water. (d) The water level is lowered again until a third resonance is heard. Calculate the length L 3 of the air column that produces this third resonance. Part V. What length of open open pipe would resonant at a fundamental frequency of 256 hz if the speed of sound was 345 m/sec? What length of open open pipe would resonant at a fundamental frequency of 512 hz if the speed of sound was 345 m/sec?
6 A hollow tube of length, open at both ends as shown above, is held in midair. A tuning fork with a frequency f o vibrates at one end of the tube and causes the air in the tube to vibrate at its fundamental frequency. Express your answers in terms of and f o. (a) Determine the wavelength of the sound. (b) Determine the speed of sound in the air inside the tube. (c) Determine the next higher frequency at which this air column would resonate The tube is submerged in a large, graduated cylinder filled with water. The tube is slowly raised out of the water and the same tuning fork, vibrating with frequency f o, is held a fixed distance from the top of the tube. (d) Determine the height h of the tube above the water when the air column resonates for the first time. Express your answer in terms of.
7 Part VI. To demonstrate standing waves, one end of a string is attached to a tuning fork with frequency 120 Hz. The other end of the string passes over a pulley and is connected to a suspended mass M as shown in the figure above. The value of M is such that the standing wave pattern has four "loops." The length of the string from the tuning fork to the point where the string touches the top of the pulley is 1.20 m The linear density of the string is 1.0 x 10-4 kg/m and remains constant throughout the experiment. (a) Determine the wavelength of the standing wave. (b) Determine the speed of transverse waves along the string. (c) The speed of waves along the string increases with increasing tension in the string. Indicate whether the value of M should be increased or decreased in order to double the number of loops in the standing wave pattern. Justify your answer. (d) If a point on the string at an antinode moves a total vertical distance of 4 cm during one complete cycle, what is the amplitude of the standing wave?
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Chapter 9 Review, pages 7 Knowledge 1. (b). (c) 3. (b). (d) 5. (b) 6. (d) 7. (d) 8. (b) 9. (a) 10. (c) 11. (a) 1. (c) 13. (b) 1. (b) 15. (d) 16. False. Interference does not leave a wave permanently altered.
(3) A traveling wave transfers, but it does not transfer.
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On the axes of Fig. 4.1, sketch the variation with displacement x of the acceleration a of a particle undergoing simple harmonic motion.
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