Statement-1: The average power transmitted by a wave on a string is proportional to the square root of the tension in the string.
Statement-2: If the amplitude of a wave on a string is doubled, the average power transmitted by it becomes four times its initial value.

Question

Statement-1: The average power transmitted by a wave on a string is proportional to the square root of the tension in the string.

Statement-2: If the amplitude of a wave on a string is doubled, the average power transmitted by it becomes four times its initial value.

TestHub · Accepted Answer

Statement-1: The average power transmitted by a sinusoidal wave on a string is given by $P_{a vg} = \frac{1}{2} μ ω^{2} A^{2} v$ . Since $v = T / μ$ , substituting $v$ gives $P_{a vg} = \frac{1}{2} μ ω^{2} A^{2} T / μ = \frac{1}{2} ω^{2} A^{2} μ T$ . Thus, $P_{a vg} \propto T$ . So, Statement-1 is true.

Statement-2: From the formula $P_{a vg} = \frac{1}{2} μ ω^{2} A^{2} v$ , it is clear that $P_{a vg} \propto A^{2}$ . If the amplitude $A$ is doubled, the average power transmitted becomes $(2 A)^{2} = 4 A^{2}$ , i.e., four times its initial value. So, Statement-2 is true.

Statement-2 is not the correct explanation for Statement-1, as they describe different dependencies of power (on amplitude and tension, respectively).

Physics - Wave on String Question with Solution | TestHub

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