## Question

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^{–12}*W*/*m*^{2} (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*/*m*^{3} and velocity of sound in air = 332*m/s*.

### Solution

From this it is clear that the ear is a extremely sensitive detector of sound waves as it can respond do amplitudes about (1/10)th the size of an atom!

#### SIMILAR QUESTIONS

A wire of uniform cross-section is stretched between two points 1 *m*apart. 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 30^{o} with the horizontal. Masses *M*_{1} and *M*_{2} are tied at the two ends of the wire. The mass *M*_{1} rests on the plane and the mass *M*_{2} 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 *M*_{1} and *M*_{2}. (g = 9.8 m/s^{2})

A copper wire is held at the two ends by rigid supports. At 30^{o}C, the wire is just taut, with negligible tension. Find the speed of transverse waves in this wire at 10^{o}C 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/s^{2})

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/s^{2}]

(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 ρ_{air}/ρ_{H} 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^{–2}kg/mol and for water vapours = 1.8 × 10^{–2} kg/mol]

(a) Find the speed of sound in a mixture of 1 mol of helium and 2 mol of oxygen at 27^{o}C. (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).

What is the maximum possible sound level in *dB* of sound waves in air? Given that density of air = 1.3 kg/m^{3}, *v* = 332 m/s and atmospheric pressure