(a) Find the speed of sound in a mixture of 1 mol of helium and 2 mol of oxygen at 27oC. (b) If the temperature is raised by 1 K to 300 K, find the percentage change in the speed of sound in the gaseous mixture. (R = 8.31 J/mol K). 


Correct option is

400.9 m/s & 0.167%


(a) In terms of temperature, the speed of sound is given by  


Now here as 1 mole of helium is mixed with 2 mole of oxygen,  



Further as helium is monatomic [CV = (3/2)R] while oxygen is diatomic (CV = (5/2)R), so for mixture   




So substituting the values of M and γ from Eqns. (2) and (3) in (1) with T= 300 K and R = 8.31 J/mol K, we get







The amplitude of a wave disturbance propagating in the positive xdirection is given by   

Where x and y are in m. The shape of the wave disturbance does not change during the propagation. What is the velocity of the wave?


A wire of uniform cross-section is stretched between two points 1 mapart. The wire is fixed at one end and a weight of 9 kg is hung over a pulley at the other end produces fundamental frequency of 750 Hz. (a) What is the velocity of transverse waves propagating in the wire? (b) If now the suspended weight is submerged in a liquid of density (5/9) that of the weight, what will be the velocity and frequency of the waves propagating along the wire?


A wire of mass  kg per metre passes over a frictionless pulley fixed on the top of an inclined frictionless plane which makes an angle of 30o with the horizontal. Masses M1 and M2 are tied at the two ends of the wire. The mass M1 rests on the plane and the mass M2 hangs vertically downwards. The whole system is in equilibrium. Now a transverse wave propagates along the wire with a velocity of 100 m/s. Find the value of masses M1 and M2. (g = 9.8 m/s2


A copper wire is held at the two ends by rigid supports. At 30oC, the wire is just taut, with negligible tension. Find the speed of transverse waves in this wire at 10oC if  


A uniform rope of length 12 m and mass 6 kg hangs vertically from a rigid support. A block of mass 2 kg is attached to the free end of the rope. A transverse pulse of wavelength 0.06 m is produced at the lower end of the rope. What is the wavelength of the pulse when it reaches the top of the rope?  


A uniform rope of mass 0.1 kg and length 2.45 m hangs from a ceiling. (a) Find the speed of transverse wave in the rope at a point 0.5 m distant from the lower end, (b) Calculate the time taken by a transverse wave to travel the full length of the rope (g = 9.8 m/s2)  


A pieze-electric quartz plate of thickness 0.005 m is vibrating in resonant condition. Calculate its fundamental frequency if for quartz,  and 


Determine the change in volume of 6 litres of alcohol if the pressure is decreased from 200 cm of Hg to 75 cm. [Velocity of sound in alcohol is 1280 m/s, density of alcohol = 0.81 g/cc, density of Hg = 13.6 g/cc and g = 9.81 m/s2]



(a) Speed of sound in air is 332 m/s at NTP. What will be the speed of sound in hydrogen at NTP if the density of hydrogen at NTP is (1/16) that of air? [Assume ρairH â‰ƒ 1.]  

(b) Calculate the ratio of the speed of sound in neon to that in water vapours at any temperature. [Molecular weight of neon = 2.02 × 10–2kg/mol and for water vapours = 1.8 × 10–2 kg/mol]


The faintest sound the human ear can detect at a frequency of 1 kHz (for which the ear is most sensitive) corresponds to an intensity of about 10–12W/m2 (the so called threshold of hearing). Determine the pressure amplitude and maximum displacement associated with this sound assuming the density of air = 1.3 kg/m3 and velocity of sound in air = 332m/s