A-sound-wave-of-velocity-350-m-s-is-directed-towards-the-surface-of-water-If-the-ratio-of-the-wave-length-of-sound-in-water-to-that-in-air-is-425-100-calculate-the-velocity-of-the-wave-in-water-

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Question Number 9954 by Tawakalitu ayo mi last updated on 18/Jan/17

$$\mathrm{A}\mathrm{sound}\mathrm{wave}\mathrm{of}\mathrm{velocity}350\mathrm{m}/\mathrm{s}\mathrm{is}\mathrm{directed}$$$$\mathrm{towards}\mathrm{the}\mathrm{surface}\mathrm{of}\mathrm{water}.\mathrm{If}\mathrm{the}\mathrm{ratio}\mathrm{of}$$$$\mathrm{the}\mathrm{wave}\mathrm{length}\mathrm{of}\mathrm{sound}\mathrm{in}\mathrm{water}\mathrm{to}\mathrm{that}\mathrm{in}$$$$\mathrm{air}\mathrm{is}425:100,\mathrm{calculate}\mathrm{the}\mathrm{velocity}\mathrm{of}\mathrm{the}$$$$\mathrm{wave}\mathrm{in}\mathrm{water}.$$

Answered by sandy_suhendra last updated on 19/Jan/17

$$\mathrm{formula}\Rightarrow \mathrm{v}=\mathrm{f}\lambda \Rightarrow \lambda =\frac{\mathrm{v}}{\mathrm{f}}$$$$\lambda =\mathrm{wave}\mathrm{length}$$$$\mathrm{f}=\mathrm{wave}\mathrm{frequency}$$$$\mathrm{v}=\mathrm{wave}\mathrm{velocity}$$$${\lambda }_{\mathrm{water}}:{\lambda }_{\mathrm{air}}=425:100$$$$\frac{{\mathrm{v}}_{\mathrm{water}}}{{\mathrm{f}}_{\mathrm{water}}}:\frac{{\mathrm{v}}_{\mathrm{air}}}{{\mathrm{f}}_{\mathrm{air}}}=17:4\Rightarrow {\mathrm{f}}_{\mathrm{water}}={\mathrm{f}}_{\mathrm{air}}$$$${\mathrm{v}}_{\mathrm{water}}:{\mathrm{v}}_{\mathrm{air}}=17:4$$$${\mathrm{v}}_{\mathrm{water}}:350=17:4$$$${\mathrm{v}}_{\mathrm{water}}=\frac{350\times 17}{4}=1,487.5\mathrm{m}/\mathrm{s}$$

Commented by Tawakalitu ayo mi last updated on 19/Jan/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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