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Water waves of wavelength $ equire{cancel} ext{ } au $ and wave speed $ v $ are related by $ v = rac{ equire{cancel} ext{ } k}{ au} $ where $ k $ is a constant - AQA - A-Level Physics - Question 7 - 2020 - Paper 1

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Question 7

Water-waves-of-wavelength-$-equire{cancel}--ext{-}--au-$-and-wave-speed-$-v-$-are-related-by-$-v-=--rac{-equire{cancel}--ext{-}-k}{-au}-$-where-$-k-$-is-a-constant-AQA-A-Level Physics-Question 7-2020-Paper 1.png

Water waves of wavelength $ equire{cancel} ext{ } au $ and wave speed $ v $ are related by $ v = rac{ equire{cancel} ext{ } k}{ au} $ where $ k $ is a constant. ... show full transcript

Worked Solution & Example Answer:Water waves of wavelength $ equire{cancel} ext{ } au $ and wave speed $ v $ are related by $ v = rac{ equire{cancel} ext{ } k}{ au} $ where $ k $ is a constant - AQA - A-Level Physics - Question 7 - 2020 - Paper 1

Step 1

Identify the formula

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Answer

The relationship between wave speed vv, wavelength au au, and the constant kk is given by:

equire{cancel} ext{ } k}{ au}$$

Step 2

Rearrange the formula to find $ k $

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Answer

To isolate kk, we can rearrange the formula as follows: k=vimesauk = v imes au

Step 3

Determine the SI units for $ k $

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Answer

The SI unit for wave speed vv is meters per second (m/s), and the SI unit for wavelength au au is meters (m). Therefore, the units for kk can be determined:

extUnitofk=extUnitofvimesextUnitofau=extm/simesextm=extm2/exts ext{Unit of } k = ext{Unit of } v imes ext{Unit of } au = ext{m/s} imes ext{m} = ext{m}^2/ ext{s}

Step 4

Select the correct option

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Answer

From the provided options, the unit m2s−1m^2 s^{-1} corresponds to the derived unit for kk. Thus, the possible SI unit for kk is:

D m2s−1m^2 s^{-1}

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