Since the outside temperature this morning is a chilly 12.0C12.0C. Bob is walkin
ID: 1583530 • Letter: S
Question
Since the outside temperature this morning is a chilly 12.0C12.0C. Bob is walking to school alone. When he reaches a distance of 158 m from the house he realizes that he forgot his backpack. So, he turns around and yells loudly, "MARY! BRING ME MY BACKPACK!!!" It so happens, however, that 0.75 s after this sound leaves his lips, Mary cranks up the volume of her favourite episode of Teenage Mutant Ninja Turtles. Does Bob's request reach Mary in time, before the sound of the show will be too loud for her to hear? And how early or late does the sound arrive?
Explanation / Answer
The speed of sound at a temperature T is given by
v = v0(1+ T/546)
where vo is the speed of sound at 00C vo = 330 m/s
v = 330( 1 - 12/546)
v = 322.7 m/s
time taken by sound to reach Mary
t = d/v
t = 158/322.7
t = 0.49 s
the time taken by sound (0.49 s) is less than 0.75 s so it will reach mary before the volume of the show goes up so Mary will be able to hear it.
to = 0.75 - 0.49 = 0.26 s
the sound reaches 0.26 s earlier