A wave travels on a string with amplitude velocity v = 90.0 cm/s.If the tension on the string is increased by 20.0%,how much would the transmitted power on the string change if the wavelength is kept constant?

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The transmitted power on a string is given by:$$P = \frac{1}{2} \mu v^2 A^2 \omega^2$$where:* $\mu$ is the linear density of the string* $v$ is the wave velocity* $A$ is the wave amplitude* $\omega$ is the angular frequencyIf the tension on the string is increased by 20.0%, the wave velocity will increase by 10.0%. This is because the wave velocity is proportional to the square root of the tension.$$v \propto \sqrt{T}$$If the wavelength is kept constant, the angular frequency will also increase by 10.0%. This is because the angular frequency is inversely proportional to the wavelength.$$\omega \propto \frac{1}{\lambda}$$Therefore, the transmitted power will increase by:$$P \propto v^2 \omega^2 \propto (1.1)^2 (1.1)^2 = 1.45$$This represents an increase of 45%.

A Wave Travels on a String with Amplitude Velocity V