2. STRING WAVES

Speed of a Wave on a String

The speed on a wave stretched under some tension, F

• The speed depends only upon the properties of the medium through which the disturbance travels

Reflection of Waves – Fixed End

• Whenever a traveling wave reaches a boundary, some or all of the wave is reflected
• When it is reflected from a fixed end, the wave is inverted
• The shape remains the same

Reflected Wave – Free End

• When a traveling wave reaches a boundary, all or part of it is reflected
• When reflected from a free end, the pulse is not inverted

Reflection and Transmission

Waves traveling along with two types of strings: a thick string with a high linear density and a thin string with a low linear density. Both strings are under the same tension, so a wave moves faster on the low-density string than on the high-density string.

(a) A wave moving from a low-density to high-density medium results in a reflected wave that is 180°(?rad) out of phase with respect to the incident pulse (or wave) and a transmitted wave that is in phase with the incident wave.

(b) When a wave moves from a high-density medium to a low-density medium, both the reflected and transmitted waves are in phase with respect to the incident wave.

Ai  > Ar     Ai > At

Interference of Waves

Two traveling waves can meet and pass through each other without being destroyed or even altered

• Waves obey the Superposition Principle

–When two or more traveling waves encounter each other while moving through a medium, the resulting wave is found by adding together the displacements of the individual waves point by point

–Actually only true for waves with small amplitudes

Constructive Interference

• Two waves, a and b, have the same frequency and amplitude

          –Are in phase

• The combined wave, c, has the same frequency and a greater amplitude

Constructive Interference in a String

• Two pulses are traveling in opposite directions
• The net displacement when they overlap is the sum of the displacements of the pulses
• Note that the pulses are unchanged after the interference