A transverse wave of amplitude $0.50 m m$ and frequency $100 H z$ is produced on a wire stretched to a tension of $100 N$ . If the wave speed is $100 m s^{- 1}$ , what average power is the source transmitting to the wire?

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Solution

$r = 0.5 m m = 0.5 \times 10^{- 3} m t$
$f = 100 H z, T = 100 N$
$v = 100 m / s$
$v = \sqrt{T / m} \Rightarrow v^{2} = (T / m) \Rightarrow m = (T / v^{2}) = 0.01 k g / m$
$P_{a v e} = 2 π^{2} m v r^{2} f^{2}$
$= 2 (3.14)^{2} (0.01) \times 100 \times (0.5 \times 10^{- 3})^{2} \times (100)^{2} \Rightarrow 49 \times 10^{- 3} w a t t = 49 m W$

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A transverse wave of amplitude 0.50 mm and frequency 100 Hz is produced on a wire stretched to a tension of 100 N. If the wave speed is 100 ms−1, what average power is the source transmitting to the wire?

r=0.5mm=0.5×10−3mtf=100Hz,T=100Nv=100m/sv=√T/m⇒v2=(T/m)⇒m=(T/v2)=0.01kg/mPave=2π2mvr2f2=2(3.14)2(0.01)×100×(0.5×10−3)2×(100)2⇒49×10−3watt=49mW

A transverse wave of amplitude $0.50 m m$ and frequency $100 H z$ is produced on a wire stretched to a tension of $100 N$ . If the wave speed is $100 m s^{- 1}$ , what average power is the source transmitting to the wire?