Question

One day, a helicopter is hovering in the air.
It is hovering in order to take important measurements and correlate
them with a nearby weather balloon. The copter is behind schedule and the
pilot is not ready to accept a late completion of task. She is skilled and
experienced and plans to manage the challenge, especially when the
experience involves no detectable wind whatsoever.
The airplane engine makes one pure sound.

As measured by airplane instruments, the sound frequency is 300 Hz.
At some moment in time, the weather balloon is observed some
detectable but immeasurable distance nearby the plane.
According to all airplane instruments, the air is stationary, but the balloon is
moving AWAY from the plane -- at a speed of 300 m/s, relative to the
plane.

Assume that, on this summer day,
sound travels at a speed of 340 m/s relative to air.
Assume, further, that the direction of in which sound travels
FROM airplane TO balloon is called "Positive".

A. Find the sound wavelength as measured by the airplane
B. Find the velocity of the sound relative to the
airplane
C. Find the sound wavelength as measured by the
balloon.
D. Find the sound frequency as measured by the balloon.

Some time later, the situation changes:
The wind has kicked up to incredibly high speeds and in a strange
direction. The result is this: According to all plane instruments,
BOTH the air and the balloon are moving away from the plane at
300 m/s. The balloon, that is, is moving at precisely the same
velocity as the air.
The pilot bails out. She attaches herself to some sort of
featherlite hanglider which can float in air. It has no engines nor
propulsion systems of any kind. She allows the air to carry her to the
airport. By some amazing twist or loophole in the laws of science
fiction, she plays a pure and lasting note of 300 Hz on her harmonica
while she travels.
All other quantities (frequency, speed of sound relative to air) are
the same as parts A-D, above.

E. What is the wavelength measured by the balloon ?
F. What is the sound velocity as measured by the balloon?
G. What is the frequency measured by the balloon ?

H. Assume that during BOTH of these previous episodes (A-D and E-
G), the plane fired 340 bullets per second directly out of its front

(rather than sending out a sound).
FOR EACH of the episodes, compute the frequency per second at
which the balloon would get hit.

Answer 1