1. Heat Capacity II Sound Velocity Method CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Instructor: Dr. Aleksey I. Filin

2. Sound Velocity v S can be expressed as: CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Heat Capacity II Sound Velocity Method Where: Heat capacity @ constant pressure Heat capacity @ constant volume R – universal gas constant T – temperature M – molecular weight Instructor: Dr. Aleksey I. Filin If we know the speed of sound, we can calculate 

3. Heat Capacity II Sound Velocity Method Vibrations transmitted through an elastic solid or a liquid or gas, with frequencies in the approximate range of 20 Hz to 20 kHz What the sound is? Definition of sound: Characteristics of sound: f – frequency [number of vibrations per unit of time, Hz, or s -1 ] – wavelength [m] Speed of sound can be found as Instructor: Dr. Aleksey I. Filin So, our goal is to measure the wavelength and the frequency of the sound By definition CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009

4. Heat Capacity II Sound Velocity Method Generator Scope Y1 t Speaker Microphone Instructor: Dr. Aleksey I. Filin Y2 Experimental Setup If the Generator output is connected to Y1 input of the Scope and the Microphone output is connected to Y2 input, the Scope shows 2 similar sin waveforms. CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009

5. Heat Capacity II Sound Velocity Method Generator Scope Y Speaker Microphone X Instructor: Dr. Aleksey I. Filin If the Generator output is connected to Y1 input of the Scope and the Microphone output is connected to X input, the Scope shows so called Lissajous pattern. A Lissajous pattern is a graph of one frequency plotted on the y axis combined with a second frequency plotted on the x axis. In our case both f are the same Experimental Setup CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009

6. Heat Capacity II Sound Velocity Method Mathematical description of the simplest Lissajous pattern Scope shows y as a function of x We know the time dependence both y and x Where  is the phase difference between y(t) and x(t) x(t) y(t)  Instructor: Dr. Aleksey I. Filin CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009

7. Heat Capacity II Sound Velocity Method Assuming X 0 =Y 0 If  = 0 y(x)=x y(x) x If  =  (a quarter of period) y 2 (t)+x 2 (t)=1 y(x) x Instructor: Dr. Aleksey I. Filin Mathematical description of the simplest Lissajous pattern CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009

8. Heat Capacity II Sound Velocity Method Assuming X 0 =Y 0 y(x)=-x y(x) x If  = 3  (three quarters of period) y 2 (t)+x 2 (t)=1 y(x) x If  =  (a half of period) Instructor: Dr. Aleksey I. Filin Mathematical description of the simplest Lissajous pattern CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009

9. Heat Capacity II Sound Velocity Method Assuming X 0 =Y 0 y(x)=x y(x) x If  = 2  (full period) Phase difference 0a quarter of period, or /4 a half of period, or /2 three quarters of period, or 3 /4 full period, or Figure on the scope Note: if X 0 = Y 0 the angle will be not 45 0 and the circles become the ellipses Full period corresponds to Instructor: Dr. Aleksey I. Filin Mathematical description of the simplest Lissajous pattern CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009

10. Heat Capacity II Sound Velocity Method Generator Scope Y Frequency is given by generator Speaker X How to measure the wavelength? Microphone Instructor: Dr. Aleksey I. Filin CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009

11. Heat Capacity II Sound Velocity Method Generator Scope Y Frequency is given by generator Speaker X How to measure the wavelength? Microphone Instructor: Dr. Aleksey I. Filin CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009

12. Heat Capacity II Sound Velocity Method Generator Scope Y Frequency is given by generator Speaker X How to measure the wavelength? Microphone Instructor: Dr. Aleksey I. Filin CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009

13. Heat Capacity II Sound Velocity Method Generator Scope Y Frequency is given by generator Speaker X How to measure the wavelength? Microphone Instructor: Dr. Aleksey I. Filin CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009

14. Heat Capacity II Sound Velocity Method Generator Scope Y Frequency is given by generator Speaker X How to measure the wavelength? Microphone Instructor: Dr. Aleksey I. Filin CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009

15. Heat Capacity II Sound Velocity Method Instructor: Dr. Aleksey I. Filin Summary We measure the shape of Lissajous pattern as a function of microphone position Distance between two positions corresponding to straight 45 0 line is equal to the wavelength of the sound in given gas at given sound frequency We calculate the speed of sound in given gas at given frequency using formula CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009