Answers Waves and Acoustics

Unit 12: Springs & Simple Harmonic Motion

Q12.1) 0.69 Hz

Q12.2) 0.0027 J

Q12.3) a) y = 6cos(4.36t)

b)

Q12.4) 306 N/m

Q12.5) a) 0.79 seconds

b) 0.99 m/s

Q12.6) a) 5.03 m/s

b) 4.79 m/s

c) 6.18 cm [above equilibrium]

Q12.7) 5

Q12.8) a) no change

b) no change

c) the period doubles

d) the period decreases by ~59%

Q12.9) 24.8 cm

Unit 13: Travelling Waves & Sound

Q13.1) 1183 Hz

Q13.2) Transverse waves displace the particles of their medium in a direction perpendicular to the direction of propagation of the wave (like waves on the surface of water). Longitudinal waves displace the particles of their medium in a direction parallel to the direction of propagation of the wave. Sound waves are longitudinal.

Q13.3) a) A = 6m, T = 1s, f = 1s, λ = 0.5m, v = 0.5m/s

b) positive

Q13.4) a)

b)

c)

Q13.5) a)

b)

c)

Q13.6) y = -6sin(2πt + 4πx)

Q13.7) y = 4sin(539t - 1.57x) [SI units]

Unit 14: Interference & Beat Frequency

Q14.1) Constructive interference occurs when waves overlap while in-phase with each other, resulting in a new wave with double the amplitude. Deconstructive interference is the exact opposite, and occurs when waves overlap while out-of-phase, resulting in the total cancellation of the wave. Active noise-cancellation headphones take advantage of this by emitting sound in an attempt to perfectly cancel incoming noise.

Q14.2)