*See attached diagram*
On straight, level, parallel tracks separated by a distance d,
two trains are testing their horns (in still air of density ρair).
The horns (located at the train fronts) emit equal frequencies.
Horn 1 is a pipe, open at one end, emitting a total power P
and resonating at its 9th harmonic. Horn 2 is a loudspeaker
of circular diameter equal to the length of horn 1.
In one test, the trains (1 and 2) and three researchers (A, B, C) are all stationary and are positioned as shown.
Sound from horn 1 takes time t to reach C, midway between the tracks.
A hears only horn 1 (loudness = β1). B (right next to A) hears both. But when both horns are sounding from
the positions shown, C hears both horns at maximum combined loudness. And if train 2 were repositioned
farther and farther forward along its track until it was exactly side-by-side with train 1, C would also hear
maximum combined loudness at 18 other positions of train 2 (including the fi nal position when the trains were
In a second test, C stands alone, still midway between the tracks. The trains (from much farther away) move
toward her at constant speeds (v2 > v1, but only v1 is known), both sounding their horns. When the two trains
are side-by-side, C notes a beat frequency of f beat .
Find the net air force (magnitude & direction) on a window pane (area = A2) on the right side of train 2.
Train 2ʼs windows were closed just before it started moving.
The list of known values: d, ρ(air) (density of air) , P (power), t, β1 , v1 , f beat , A2
The Attempt at a Solution
By working backward I know I have to find the velocity of train 2 in order to find the F exerted by the wind on the window. In order to find the velocity I need to use the doppler shift equation, however in order to find the frequency of train 2 I need the wavelength of its train horn.
Any help would be appreciated. Thanks.
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