a) Using the known values R=8.31 joule.mole-1.k, =1.40 and M=28.8*10^-3Kg for ai

Question

a) Using the known values R=8.31 joule.mole-1.k, =1.40 and M=28.8*10^-3Kg for air, calculate the velocity of sound in air at 0 C. How well does this predicted value agree with your value determined from this experiment ?

b) What are the shortest and the longest wavelengths of audible sound in air at 0 C?

c) It is possible to produce ultrasonic waves with frequencies as high as 6*10^8 Hz. Calculate the wavelength of such a sound wave and compare its value with those of visible light, which range from 4*10^-5 cm to 7*10^-5 cm.

Explanation / Answer

Speed of sound in air, v = sqrt(*Rair*T)
T = 273.15 K
=1.40

R = M*Rair
Rair = 8.314/(28.8*10^-3) = 288.7 J/kg k

v = sqrt(1.4*288.7*273.15)
v = 332.3 m/s

It is very close to the predicted value which is 331.3 m/s

(b)
Assuming the speed of sound in air to be 331.3 m/s
We know, wavelength = speed/frequency,

The longest wavelength for a human with average hearing capacity (20 Hz to 20,000 Hz) = 331.3/20 =16.565 m.
The shortest wavelength would be 331.3/20000 = 0.1656 m =16.56 cm

(c)
f = 6 * 10^8 Hz
Wavelength = v/f
= 331.3/( 6 * 10^8 )
= 5.52 * 10^-7 m
= 5.52 * 10^-5 cm

It lies btw the visible light range.

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