Question Number 10713 by Saham last updated on 23/Feb/17
$$\mathrm{y}\:=\:\mathrm{5sin}\left(\mathrm{2000}\pi\mathrm{t}\:−\:\mathrm{0}.\mathrm{4x}\right),\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{wavelength} \\ $$
Answered by ridwan balatif last updated on 23/Feb/17
$$\mathrm{y}=\mathrm{5sin}\left(\mathrm{2000}\pi\mathrm{t}−\mathrm{0}.\mathrm{4x}\right) \\ $$$$\mathrm{base}\:\mathrm{formula}'\mathrm{s}\:\mathrm{y}=\mathrm{Asin}\left(\omega\mathrm{t}−\mathrm{kx}\right) \\ $$$$\mathrm{A}=\mathrm{5} \\ $$$$\omega=\mathrm{2000}\pi \\ $$$$\mathrm{k}=\mathrm{0}.\mathrm{4} \\ $$$$\frac{\mathrm{2}\pi}{\lambda}=\frac{\mathrm{2}}{\mathrm{5}} \\ $$$$\lambda=\mathrm{5}\pi\:\rightarrow\mathrm{wavelength} \\ $$
Commented by Saham last updated on 23/Feb/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$
Answered by mrW1 last updated on 23/Feb/17
$${A}=\mathrm{5}\:{m} \\ $$$$\omega=\mathrm{2000}\pi \\ $$$${k}=\mathrm{0}.\mathrm{4} \\ $$$${frequency}\:{f}=\frac{\omega}{\mathrm{2}\pi}=\frac{\mathrm{2000}\pi}{\mathrm{2}\pi}=\mathrm{1000}\:{Hz} \\ $$$${wave}\:{length}\:\lambda=\frac{\mathrm{2}\pi}{{k}}=\frac{\mathrm{2}\pi}{\mathrm{0}.\mathrm{4}}=\mathrm{5}\pi=\mathrm{15}.\mathrm{7}\:{m} \\ $$$${wave}\:{speed}\:{v}=\lambda{f}=\mathrm{15}.\mathrm{7}×\mathrm{1000}=\mathrm{15700}\:{m}/{s} \\ $$
Commented by Saham last updated on 23/Feb/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$