5. KEY EQUATIONS
• Wave speed (v) v = λf = ω/k
• Wave number (k) k=2π/λ
• Frequency (f) f=1/T
• Wavelength (λ) λ=2π/k
• Position (x)
• Angular frequency (ω) ω=2πf=2π/T
• Period (T)
• Amplitude (A)
• Phase constant (φ)
6. KEY EQUATIONS
• Displacement (D) D(x,t)= Asin(kx-ωt+φ)
• Instantaneous speed (μ) μ(x,t)= -ωAcos(kx-wt+φ)
• Acceleration (a) a(x,t)= -ω2Asin(kx-ωt+φ)
• Kx-wt is wave travelling in the direction of increasing x
• Kx+wt is wave travelling in the direction of decreasing x
7. QUESTION 1
• Nick tries to talk to Susan in the classroom, and dolphin
A tries to communicate to dolphin B in the sea water.
Determine the wavelength of of the sound wave in the
air and in the sea water? Whose sound wavelength is
longer?
• The speed of sound wave in air is 343 m/s
• The speed of sound wave in sea water is 1560 m/s
• Frequency of sound wave is 500 Hz
8.
9. SOLUTION
• v = λf or λ = v/f
• λair = vair/f = 343m/s / 500 Hz = 0.686 m
• λsea water = vsea water /f = 1560m/s / 500 Hz = 3.12 m
• The wavelength of the sound wave of the dolphin A is
longer than the wavelength of Nick.
10. QUESTION 2
• The guitar string has the length of 1.5m long and it is vibrating in
harmonic motion. The string vibrates with 30 complete
vibrational cycles in 10 seconds. Determine the frequency,
period, wavelength and wave speed of this wave.
