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Wave Model · Paper 2 — Free Physics SL Practice Questions

1FoundationSAQ-LWave equations4 marksPaper 2~6 min

A wave is generated in a ripple tank. The displacement of the water surface is given by

y(x,t) = 0.0050 \sin(12x - 8t)

where

x

is in metres,

t

is in seconds, and the amplitude is in metres. For deep-water waves, the wave speed is given by

v_{\text{deep}} = \sqrt{\dfrac{g\lambda}{2\pi}}

, where

g = 9.81 \text{ m s}^{-2}

(a)

(i) Determine the wavelength and frequency of the wave. [2]
(ii) Determine the wave speed. [1]
(iii) Determine the maximum speed of a water particle in the medium. [1 mark]

(b)

Calculate the theoretical deep-water wave speed for this wavelength. Hence evaluate whether this wave behaves as a deep-water wave. [2 marks]

(c)

The wave generator frequency is doubled while the water depth remains unchanged. The new wavelength is

0.262 \text{ m}

. Using the deep-water formula, calculate the theoretical deep-water speed for the new wavelength. Evaluate whether doubling the frequency makes the wave more or less consistent with deep-water behaviour, justifying your answer by comparing both wave speeds with their respective deep-water predictions. [1 mark]

Solutions

2MasterySAQ-STypes of waves: Transverse and longitudinal4 marksPaper 2~6 min

An earthquake generates P-waves and S-waves simultaneously at the epicentre. P-waves travel through the Earth's interior at

v_\text{P} = 5.0 \text{ km s}^{-1}

. S-waves travel at

v_\text{S} = 3.0 \text{ km s}^{-1}

. A seismometer detects the P-wave arrival 4.0 s before the S-wave arrival.

(a)

State the difference in the direction of particle oscillation between P-waves and S-waves. [1 mark]

(b)

S-waves cannot travel through the liquid outer core of the Earth. (i) State the physical property that liquids lack which prevents S-wave propagation. [1]
(ii) Explain, using your answer to (b)(i), why S-waves cannot propagate through the liquid outer core. [1 mark]

(c)

Determine the distance from the earthquake epicentre to the seismometer. [2 marks]

Solutions

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