Question

If the frequency and amplitude of a transverse wave on a string are both doubled, then the amount of energy transmitted through the string is

• A. doubled
• B. become 4 time
• C. becomes 16 times
• D. becomes 32 times

Answer 1

Answer: (C)

becomes 16 times

Energy transmitted through the string $E\propto {\nu }^2{A}^2$

Now, ${\nu }^{\prime }=2\nu A^{\prime }=2A$

Thus, $\frac{E^{\prime }}{E}=\frac{\left({\nu }^{\prime }{)}^2\right(A^{\prime }{)}^2}{{\nu }^2{A}^2}=\frac{4{\nu }^2\times 4A^2}{{\nu }^2{A}^2}$

$⟹E^{\prime }=16E$