I think Don's question is a good one. Assuming the typical things---no air resistance, parabolic arc, smooth surfaces, all that---the horizontal component of the pebble shouldn't change at all, throughout the trajectory. So, if the amount of sound generated depends only on the kinetic energy of the pebble, it's definitely at the top of the arc that you'd want the thing to hit for the least noise generated.
If there is *traction* between the pebble and window allowed, that could definitely bring in some extremely tricky effects, including higher-order modes excited in the window (vibrational modes are the only things I can think of, in a linear approximation, which should lead to sound production), and even suppression of certain modes due to things like waveguide effects or Lamb modes. Once one gets to that level of analysis, though, it's almost impossible to convince anyone that their model is a nearly complete representation of reality, and even graduate students in physical acoustics would have an extremely hard time accounting for all the effects possible.
/************************************
Down with categorical imperative!
flutzpah@yahoo.com
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----- Original Message ----
From: "DMathies@tulsacc.edu" <DMathies@tulsacc.edu>
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Sent: Monday, August 25, 2008 9:49:50 AM
Subject: Re: [Phys-l] One of those Yahoo Answers "URGENT" Physics problems (with a twist)
Blame that one on me I wrote the question. Now that you point it out you
may be correct. I was thinking that the lowest velocity would generate the
least noise. I really don't know.
Don Mathieson
Tulsa Community College
dmathies@tulsacc.edu
Steve Highland <shighlan@uslink.net>
Sent by: phys-l-bounces@carnot.physics.buffalo.edu
08/25/2008 10:42 AM
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Subject
[Phys-l] One of those Yahoo Answers "URGENT" Physics problems (with a
twist)
I¹ve been horsing around on Yahoo Answers a little bit today and I came
across this question;
------------
Jack is chucking pebbles gently up to Sarah's window, and he wants the
pebbles to hit the window with only a horizontal component of velocity. He
is standing at the edge of a rose garden 8.00 meters below her window and
11.0 m from the base of the wall. How fast are the pebbles going when they
hit her window?
------------
Of course this is an easy problem for a non-beginner. What interests me
is
the assumption that throwing the pebble so it hits the window horizontally
is the ?gentlest¹ throw. I don¹t think so. I would think lobbing the
pebble higher than the window so it came down and struck the pane at a
glancing angle would actually be a gentler impact. But I'm not 100% sure.
It would hit with a lesser horizontal velocity and deliver less of an
impulse to the window, but is that the only thing that matters? I doubt
it.
The duration of contact with the window must play a role, and that time
must
get shorter with higher vertical speeds, right? That would seem to
increase
the force and be bad for the window.
What does govern how ?gently¹ the pebble hits the window? Is my instinct
that a glancing blow at higher speed is gentler than a head-on impact at a
slower speed right or wrong?