Speed of Sound Lab Report Jamie Cook PHYS 1114: college Physics I Oklahoma City Community College December 10, 2013 Purpose: The purpose of this experiment is to measure the speed of sound in air and to determine the effects of frequency on the speed of sound.
Apparatus (equipment usea Signal generator: manufacturer- EMCO, model number- SS-I, range- 20Hz-2MHz, least count- 1 Hz Frequency meter: manufacturer- DEADALON CORPORATION, model number- NIA, range- 20Hz-2MHz, least count 1 kilohertz Oscilloscope: manufacturer- BK Precision, model number- 1472C, range- 0-15MHz, least count- 1 Hz Speaker: anufacturer- Western Electric, model number- D17312, range- NIA, least count- N/A Microphone: manufacturer- Western Electric, model number- D17312, range- NIA, least count- N/A Method: Experimental: In order for this equipment to assist one in measuring the speed of sound, the speaker and microphone are positioned inside the hollow tube with the speaker stationary at one end. The microphone is able to be moved and set a chosen distance from the speaker, from almost touching to 1 meter. The signal generator is connected to the speaker by a pair of wires. From this pair of wires, another pair of wires onnects the signal generator to the frequency meter.
A set of wires also run from the signal generator to the oscilloscope. A separate set of wires is connected from the oscilloscope to the microphone inside the tube. The set up of the equipment allows for the output of the signal meter to be read and measured by the frequency meter while being led to the speaker. This input causes the speaker to vibrate, which produces sound waves inside the tube. These sound waves, picked up by the microphone, are then sent to the oscilloscope as a signal. A pattern is displayed on the screen of the oscilloscope. With the signals in phase, the patterned displayed is a straight diagonal line. With the signals out of phase, the pattern displayed is elliptical.
The straight diagonal line will be displayed when the microphone is positioned at one wavelength from the speaker, and the distance from the end of one wavelength to the next through the length of the tube. In this experiment, the signal generator was set so that the frequency meter showed a reading of 1,803 Hz. The microphone was moved to a distance from the speaker so that the oscilloscope displayed a straight diagonal line. This position was of the microphone was recorded as the initial position, or beginning of a wavelength. The microphone was then moved farther in the same direction until the oscilloscope displays the same horizontal line.
This position was recorded as final position, or the end of the wavelength. The distance between the two positions represents one wavelength for this frequency. This was repeated for frequencies of 2,402 Hz, 3,002, Hz, 3,602 Hz, and 4,201 Hz. Method continued: Data analysis: Atter tne posltlons were recoroea Tor Trequencles 1 Hz, and 4,201 Hz, the wavelength was determined for each. This was done by ubtracting the initial position from the final position (position final-position initial??”wavelength). Using the calculated wavelength, the speed of sound in air at each frequency was determined by multiplying the wavelength by the frequency (speed of sound??”wavelength x frequency).
By adding the five speed values and dividing by the number of speeds, the average speed of sound was calculated. Then 344 m/s was used as the accepted speed of sound in air to calculate a theoretical wavelength for each frequency. Percent discrepancy between measured wavelength and theoretical wavelength was calculated (% discrepancy = ((measured-theoretical)/ heoretical) x 100). A graph of velocity versus frequency was plotted using the recorded data and used to determine how speed of sound varies depending on the frequency. Results: Part I of experiment: Frequency Initial Position (m) Final Position Wavelength (distance from initial position to final position) Speed of sound in air (wavelength x frequency) (m/s) 1 ,803 HZ 19. cm = 0. 194m 38. 6crn = 0. 386m = 0. 192m 0. 192m x 1803 HZ = 346. 21M 2402 HZ 7. 7crn = 0. 077m 22 cm = 0. 22m 0. 22m-o. onrn = 0. 143m 0. 143m x 2,402 HZ = 343. 7m,’s 3,002 HZ 12. 9crn = 0. 129m 24. 4cm = 0. 244m 0. 244111-0. 29m = 0. 115m 0. 115m x 3,002 HZ = 345. 2m,’s 3,602 HZ 7. 3crn = 0. 073m 16. 9cm = 0. 169m o. 169111-0. 073m = 0. 096m 0. 096m x 3,601 HZ = 345. 7m,’s 4,201 HZ 13. 1cm -0. 131m 21. 3crn = 0. 213m 0. 213t-n-o. 313m = 0. 082 0. 082m x 4,201 HZ = 344. 5m,’s Average Speed of Sound (speed of sound for each frequency divided by the number of speeds (5)) (m/s) 346. 2m,’s +343. 7m,’s + 345. 2m,’s + 345. 7m,S+ 344. 5m,’s 5 speeds 345. rms Results continued: Part II of experiment: Theoretical wavelength (wavelength = velocity divided by frequency, using 344m/s as accepted speed of sound in air) (m) Measured wavelength % Discrepancy between measured and theoretical wavelengths ((measured-theoretical divided by theoretical) multiplied by 100) 344t-n,’s 11803 HZ = 0. 1908 0. 192m x 100 = 0. 639% 344t-n,’s 12,402 HZ = 0. 1432 0. 143m ((0. 143m-o. 1432myo. 1432m)x 100 = 0. 140% 344t-n,’s 13,002 HZ = 0. 1 145 0. 115m ((0. 11 5t-n-o. 1145myo. 1145m) x 100 = 0. 437% 344t-n,’s 13,602 HZ = 0. 0955 0. 096m ((0. 096m-o. 0955myo. 0955m) x 100 = 0. 524% 344t-n,’s 14,201 HZ = 0. 0819 0. 082m ((0. 082m-o. 0819myo. 0819m) x 100 = 0. 122% Part Ill 0T experiment: See “Velocity Versus Frequency’ graph attached