## Question

A wave pulse starts propagating in +*x*-direction along a non-uniform wire of length 10 m with mass per unit length given *m* = *m*_{0} + α*x* and under a tension of 100 *N*. Find the time taken by the pulse to travel from the lighter end (*x* = 0) to the heavier end. (*m*_{0} = 10^{–2} *kg/m* and α = 9 × 10^{–3} *kg/m*^{2})

### Solution

2.335 sec

Velocity of transverse wave in a string,

Integrating within proper limits,

= **2.335 sec**.

#### SIMILAR QUESTIONS

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).

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*.

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

(a) The power of sound from the speaker of a radio is 20 *mW*. By turning the knob of volume control the power of sound is increased to 400 *mW*. What is the power increase in *dB* as compared to original power?

(b) How much more intense is an 80 dB sound than a 20 dB whisper?

A window whose area is 2 *m*^{2} opens on a street where the street noise result in an intensity level at the window of 60 dB. How much ‘acoustic power’ enters the window via sound waves. Now if an acoustic absorber is fitted at the window, how much energy from street will it collect in five hours?

A dog while barking delivers about 1 *mW* of power. If this power is uniformly distributed over a hemispherical area, what is the sound level at a distance of 5 m? What would the sound level be if instead of 1 dog, 5 dogs start barking at the same time each delivering 1 *mW* of power?

An observer is at a distance of one metre from a point light source whose power output is 1 kW. Calculate the magnitude of electric and magnetic fields assuming that the source is monochromatic, it radiates uniformly in all directions and that at the point of observation it behaves like a travelling plane wave. Given that *H/m* and

Decibel is: