Sect 11 7 Wave Motion Lab Various kinds

Sect. 11 -7: Wave Motion (Lab!) • Various kinds of waves: – Water waves, Waves on strings, etc. • Our interest here is in mechanical waves. – Particles of matter move up & down or back & forth, as wave moves forward. • General feature: – Wave can move over large distances BUT particles in medium through which wave travels move only a small amount

Conceptual Example 11 -10 • Is the velocity of a wave moving along a cord the same as the velocity in the cord? NO!!

• Waves require a medium though which to propagate. • Waves carry energy (through the medium). • The energy must come from some outside source. • The source is usually a vibration (often a harmonic oscillation) of the particles in the medium. • If the source vibrates in SHM, the wave will have sinusoidal shape in space & time: – At fixed t: Position dependence is sinusoidal – At fixed position x: Time dependence is sinusoidal.

• Wave velocity v velocity at which wave crests (or any part) move. v particle velocity. Period : T = time between crests. Frequency: f = 1/T Wavelength: λ = distance between crests λ = v. T or v = λf

v = λf or λ = v. T • Frequency f & wavelength λ depend on properties of the source of the wave. • Velocity v depends on properties of medium: String, length L, mass m, tension FT: v = [FT/(m/L)]½ • Example 11 -11

Sect. 11 -8: Longitudinal & Transverse Waves

Longitudinal Waves Sound waves: Longitudinal mechanical waves in a medium (shown in air) Still true that v = λf λ = v. T or

• For longitudinal & transverse waves we always have: v = λf or λ = v. T • As for waves on string, the velocity v depends on properties of the medium: String, length L, mass m, tension FT: v = [FT/(m/L)]½ Solid rod, density ρ, elastic modulus E (Sect. 9 -5): v = [E/ρ]½ Liquid or gas, density ρ, bulk modulus B (Sect. 9 -5): v = [B/ρ]½ – Example 11 -12

• Water waves: Surface waves. A combination of longitudinal & transverse:

Sect. 11 -9: Energy Transport by Waves • For sinusoidal waves: Particles in the medium move in SHM, amplitude A. From SHO discussion, we know: E = (½)k. A 2 Energy in wave (wave amplitude)2 • Define: Intensity of wave I: I (Power)/(Area) = (Energy/Time)/(Area) I A 2

Spherical Waves

• Intensity of spherical wave: I (1/r 2) (I 2/I 1) = (r 1)2/(r 2)2 • Also: I A 2 Amplitude A (1/r) (A 2/A 1) = (r 1)/(r 2) • Example 11 -13