Mahima Kapoor Physics 101 - L2G (LO4)

1. Question 1:
a) A skydiver dives out of a plane from an altitude of 2500 m. The temperature
at this point is 10 degrees Celsius and the speed of sound is 280 m/s. When
the skydiver is at an altitude of 1000 m the temperature is 20 degrees
Celsius, what is the speed of sound at this temperature?
b) If the skydiver began screaming (with a gradually increasing pitch), would
the sounds arrive at different times or the same time, depending on how far a
spectatorstands?
c) If the skydiver was a deep-sea or scuba diver, how would the speed of sound
be altered (i.e. What effect does being in a different medium have) ?
Explain.

2. Question 1:
a) In an attempt to answer this question effectively, it is important to recall that density of
air is inversely proportional to the temperature (in Kelvins) and that the speed of sound is
related to the density as evident from the equation: 𝑣 = √
𝐵
𝑝
. Thus, we are given the
relationship that 280 m/s = √
𝐵
𝑝
and since p= 1/T we have that p=1/283
therefore, 280 m/s = √
𝐵
1/283
and solving for B (bulk modulus) we get B =
277.03 and since the ratio of change in pressure divided by the fractional
change in volume is constantwe can substitute B back into the equation to
get 𝑣 = √
277.03
1/293
= 284.9 m/s at 20 degrees Celsius.
b) To answer this conceptual question it is important to realize that the speed of sound
waves are not wavelength-dependant in air shown by the equation 𝑣 = √
𝐵
𝑝
. Thus,
different pitches of sound would arrive at the same time regardless of the
distance away a spectatorwas. However, it is also important to note that if
the speed of sound in air was wavelength dependant then the different
pitches of sound of the screaming skydiver would arrive at different times
depending on how far away you were from the source.
c) To answer this question is it crucial to consider the effect a medium has on
the speed of sound travel. Evident from the equation 𝑣 = √
𝐵
𝑝
, where
B=bulk modulus, p= density, and v= speed of sound, the speed of sound
is dependent on the density of the medium it is in. Recall the trend of the
speed of sound in different mediums. Conventionally, the speed of sound
increases as the density of the medium increases (i.e. from solid to liquid to
gas). So, if the skydiver was scubadiver instead the speed of sound
underwater would increase (i.e. sound would travel faster in water than in
air).
Sources cited: www.kongtakane.net