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"Answer This" Questions

Chapter 1

1-C. Wave motion versus medium motion.

If a very small ribbon is glued at a point on a rubber rope and an impulsive wave is sent along the rope from left to right, what will happen to the ribbon?
a) It will move with the medium velocity.
b) It will travel down the rope from left to right.
c) It will not move.
d) It will move with the wave velocity.
e) It will travel at 760 mph.



a) The ribbon is attached to the medium, the rubber rope itself. When a wave propagates down the rope, the medium moves up and down while wave energy moves to the right. The rope itself does not move to the right, just the bulge of displacement of the rope caused by the impulsive wave. First the bulge is at the left and later it is farther to the right. The ribbon stays at a fixed position x, which does move up and down.

The following animation shows this is detail. If the animation is not moving click on the Reload button.

The ribbon is represented by a black dot. As the pulse moves to the right and passes the dot, the dot lifts up and back down with the medium.


1-D. Wave velocity.

A rubber rope 15 feet long is tied to the wall. It takes an impulsive wave 3 seconds to travel down the rope, reflect, and come back to where it started. What is the wave velocity in feet per second (ft/s)?
a) 5 ft/s
b) 10 ft/s
c) 15 ft/s
d) 20 ft/s
e) none of these

A mass on a spring bobs down and back up 40 times in 10 seconds. What is its frequency in Hertz?



Part 1. b) The distance traveled in 3 seconds is 30 feet, twice the length of the rope, because it reflected and came back to where it started. The wave velocity or speed is thus 30 ft/3 s = 10 ft/s.

Part 2. The mass on the spring undergoes 40 cycles in 10 seconds, so the frequency is 40/10 cycles per second = 4 Hz.


1-H. What can you change?

You are given a wave medium with fixed elasticity and density. A traveling sinusoidal wave can be created in this medium
a) of any frequency.
b) of any wavelength.
c) of any wave velocity.
d) both a and b.
e) a, b, and c.

If you want to make a wave in a string move very fast (i.e., have a large wave velocity), you can
a) make the tension in the string large.
b) use a thin rather than thick string.
c) jiggle your hand fast to create the wave.
d) a and b.
e) a, b and c.



Part 1. d)The wave velocity depends on the properties of the medium, especially elasticity and inertia. The more elastic the medium is, and the less the mass density, the faster the wave travels. So, if those are "given" properties of the medium, we cannot change them or the wave velocity. However, one can change the frequency of the wave by changing how you make it. If I am making a wave on a rubber rope, I can shake my hand up and down faster to raise the frequency. If I increase the frequency, the wavelength becomes shorter. Thus I can control wavelength as well as frequency.

Part 2. d) Wave velocity is determined by elasticity and inertia. If I stretch the string tighter or have a less dense string, the wave will move faster. Shaking it up and down at a higher frequency does not change the wave velocity.


1-I. Pressure

A hammer hits on the top of a nail with a force of 50 pounds. The nail tip pressing against a piece of wood has an area of 0.01 sq. in. A force of 100 pounds is applied to the top of a uniform cylinder having an area of 1 sq. in. Which exerts the greater pressure on the wood and by how much?
a) The pressure of the nail is 100 times greater than that of the cylinder.
b) The pressure of the nail is 50 times greater than that of the cylinder.
c) The pressure of the cylinder is 2 times greater than that of the nail.
d) The pressure of the cylinder is 100 times greater than that of the nail.



b) Pressure is force per unit area. To find the pressure applied by the nail, divide the force, 50 pounds by the nail tip area, 0.01 sq. in. to get P = 50/0.01 lbs/in2 = 5000 lbs/in2. For the cylinder P = 100/1 lbs/in2 = 100 lbs/in2. So the nail exerts 5000/100 = 50 times more pressure.


1-J. Sounds through a wall

Sometimes you can faintly hear somebody speaking behind a wall in the room next to you, because
a) air molecules penetrate the wall and transmit the sound wave.
b) sound waves can sneak through tiny openings in the wall.
c) part of the original sound wave is transmitted through the wall.
d) the original sound wave breaks apart when it hits the wall, and regenerates itself on the other side of the wall.
e) none of the above.



c) Sound is a vibration of the air molecules such that the density and pressure changes are carried along as a wave. When the sound wave hits the wall, it compresses (or rarefies) slightly the material in the wall and sound travels in the solid material of the wall. Sometimes the material of a wall, if thin enough, does not compress but just bends in and out so that it compresses the air on the opposite side transferring the sound wave through the wall in that fashion. In either case the sound has been transmitted through the wall and c) is the correct answer.

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© William J. Mullin