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1. Oscillations and Waves

(a) Explain what oscillations are and, separately, what a wave is

(b) Explain the distinction between longitudinal and transverse waves.

(c) You are given the following expression for the position of an oscillating body:

z(t) = A(1) cos wt

where is the time variable.

i. If A(t) = A and are constant in time, what kind of oscillatory

motion is described by z(t)? What would

represent in such

a case? Give its explicit expression as a function of the elastic

constant & and the mass of the oscillator.

ii. If A(t) = Act, with > 0, 4 and constant in time, what

kind of oscillatory motion is described by z(t)? What would w

represent in such a case? Give its explicit expression with re-

spect to μ, k and m.

(d) A travelling harmonic wave may be described by the equation:

where the position, the time and all quantities, including the con-

stants , and y, are in SI units. For this wave, write down each of

the following physical quantities - in terms of one or more of a, 3 and

Y- and briefly explain its meaning:

i. The amplitude.

ii. The wavelength. Specify its Sl units.

iii. The frequency. Specify its SI units.

iv. The speed. Specify its Sl units.