Aashish SinghalUB Person- 50122537

Lab ReportExperiment MP1: Speed of Sound

Length of the tube l = 131.3 cmDiameter of the tube = 7.4 cm radius (r) = 3.7 cmEstimated (m = 2) frequency = 123.5 HzEffective length of tube = l + 1.2r = 1.357 m

VI-1The frequency was determined, corresponding to first 10 harmonics, starting from m = 2 all the way to m = 20, in increments of 2.Table:m2468101214161820

f (Hz)122.3253.5378.3510.3637.8768.21021.11152.51273.51414.7

Plot of frequency ( f ) v/s m:Using LINEST,Slope = s = 73.653Slope Uncertainty = s = 1.96308Using v = s*4*leffleff = 1.357 m and leff = 0.01 mv = (73.653)*4*(1.357)

v = 399.78848 m/s

v/v = v = v*

v = 399.78848*0.02765v = 44.2215 m/s

So, v = 399.78848 44.2215 m/s

VI-2 The frequency was determined, corresponding to first 10 harmonics, starting from m = 1.Table:m135791113151719

f (Hz)60.2195.5326.9462.5583.2706.8841.6911.51076.21276.4

Plot of frequency (f) v/s m:

Using LINEST,Slope = s = 64.529Slope Uncertainty = s = 1.546893Using v = s*4*leffleff =1.357 m and leff = 0.01 mv = (64.529)*4*(1.357)

v = 350.2634 m/s

v/v = v = v*

v = 350.2634*v = 35.1372 m/s

v = 350.2634 35.1372 m/s

VI-3 The voltage reading of the DMM was measured every 5 cm of the tube, keeping both the ends of the tube open. Table (Corresponding to m=4)

X (cm)V (v)X (cm)V (v)X (cm)V (v)X (cm)V (v)

50.0221400.0591750.02341100.0533

100.034450.0571800.03951150.0490

150.0430500.0490850.04381200.0423

200.0474550.0382900.04871250.0295

250.0516600.0223950.05081300.0125

300.0546650.00561000.0510

350.0575700.01281050.0513

Plot : (Using EXCEL)

VI-4 The voltage reading of the DMM was measured every 5 cm of the tube, covering the end of the tube, furthest from the speaker. (Corresponding to m=5)

Table:x (cm)V (v)x (cm)V (v)x (cm)V (v)x (cm)V (v)

50.0087350.0114650.0129950.0065

100.0129400.0072700.01551000.0017

150.0153450.0024750.01591050.0022

200.0170500.0019800.01491100.0067

250.0168550.0065850.01331150.0056

300.0148600.0099900.01041200.0090

Plot: (Using EXCEL)

V-5The function generator was set to m=10 frequency. The frequency was varied by 5 Hz and the voltage readings were recorded.Table:f(Hz)(V^2)f(Hz)(V^2)f(Hz)(V^2)f(Hz)(V^2)

5408.10E-055802.25E-066203.97E-056496.89E-05

5451.69E-065852.89E-066256.89E-056552.12E-05

5501.44E-065906.25E-066301.04E-046602.03E-05

5553.24E-065955.76E-066332.10E-046651.09E-05

5602.25E-066008.41E-066361.80E-046706.25E-06

5651.69E-066059.61E-066391.96E-046754.84E-06

5702.56E-066101.16E-056421.54E-046803.61E-06

5751.96E-066153.14E-056469.13E-056851.96E-06

Plot: (Using Excel)

Am2= 2.10E-04 V2fm= 633 HzAm2/2 = 1.05E-04 V2Consider, f1 = 630 Hz and f2 = 642 HzTherefore, f = f2-f1 = 12 HzConsider the uncertainties to be: fm =0.1 Hz and f =2 HzQ= fm/f = 633/12=52.75 Q=52.75Q/Q= Q =Q* Q =Q* 0.16667Q=8.79167Q = 52.75 8.79167