power in wave

Question

Power transmitted by a sinusoidal wave on a string increases with?

RankGuru · Accepted Answer

1. **Average Power Formula**: For a string of linear density $\mu$ and wave speed $v$, the average power is $P = \frac{1}{2} \mu \omega^2 A^2 v$.
2. **Variables Check**: 
   - $\omega = 2\pi f$ (angular frequency)
   - $A$ = amplitude
3. **Proportionality**: Sustituting $\omega$ gives $P \propto A^2 f^2$.
4. **Conclusion**: Power is directly proportional to the **Square of the amplitude** and the **Square of the frequency**.
5. **Impact**: Increasing both $A$ and $f$ by a factor of 2 leads to a $16$-fold increase in power transmitted.

Rank Guru

power in wave

Select the correct option: