Please show work for how you came up with the answer if possible. Thank you. U9Q

Question

Please show work for how you came up with the answer if possible. Thank you.

U9Q1 Within a resonance tube antinodes are measured to be at 3 cm and 14.5 cm using a frequency of 1500Hz. What would be the measured speed of sound? A) 172.5 ms B) 17250 m/s C) 345 m/s At an air temperature of 27° what is the expected speed of sound.

A) 347.9 m/s B) 331.7 m/s C) 358.7 m/s U9Q3 D) 34500 m/s D) cannot be determined

U9Q2 A 60 cm long metal bar is clamped at its center. The expected wavelength created when the bar is struck along its length is A) 0.6 m B) 0.3 m C) 1.2 m d) 0.9 m U9P1

A 605 gram aluminum bar has the following dimensions length 0.75 m, width 0.010 m and height 0.030 m. The bar is clamp at its center and struck along its length, the measured frequency is found to be 3333 Hz. Determine the measured speed of sound within the metal bar.

The Young’s modulus for aluminum is 6.7x1010. Determine the theoretical speed of sound for the metal bar.

Explanation / Answer

Q1.

distance between aninoded = wavelength / 2

(14.5 - 3) = lambda / 2

lambda = 23 cm = 0.23 m

speed = lambda * frequency = 0.23 x 1500 = 345 m/s

Ans(C)

Q2)

now both points will work as nodes.

so wavelength = 2L = 2 x 0.60 = 1.2 m

Q5) wavelength, lambda = 2x 0.75 = 1.5 m

f = 3333 hz

speed = lambda * f = 4999.5 m/s

and speed = sqrt( yooung modulus / density )

Y = 6.7 x 10^10 Pa

density = M / V = (0.605) / (0.75 x 0.01 x 0.03) = 2688.89

v = sqrt( 6.7 x 10^10 / 2688.89 ) = 4991.73 m/s

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