Question

rage of 5 Problem 2: The speed of sound in a certain metal is vm. One end of a long pipe of that metal of length L is struck a hard blow. A listener at the other end hears two sounds, one from the wave that travels along the pipe's metal and the other from the wave that travels through the air inside the pipe. (a) If v is the speed of sound in air, what is the time interval At between the arrivals of the two sounds at the listener's ear? (b) If At = 0.750 s, and the metal is steel and the air temperature is 30 °C, what is the length L? (The bulk modulus of steel is about 13.9x1010 Pa, and its density is 8.05x10kg/m3)

Answer 1

Answer :

Given that

metal of length L is struck a hard blow

v is the speed of sound in air

  $\Delta$t is the arrivals of two sounds at the ear

  $\Delta$t =0.750 s

temperature is 30 o C

Cal let 'l' meter is length of pipe, speed of sound in steel r=562 Where & is bulk modules of metal pis density of metal V= 13.9x Polo 113 ✓ 8105 x103 13 9000000000 J 8050 10.5 :- (17267080.75) : ; 1412 x10° mis = 4200 m/s At = (2+)-(2/km) Where too is taken by sound to cover distance w through åteed,

taken by sound to cover 4r is time distance Ľ through air coloumn. (b.) last part. L= at (+1-(1m)) = 0.750 (11349) - (V4200) = 0.760 (6-0029) — 21380x104] 50.750 (0.002672) L=0.002004 m