Physics: Atransverse traveling wave on a taut wire has an amplitude of 0.200 mm and a frequency of 500 hz. it travels with a speed of 196 m/s. (a) write an equation in si units of the form y 5 a sin (kx 2 vt) for this wave. (b) the mass per unit length of this wire is 4.10 g/m. find the tension in the wire.

Atransverse traveling wave on a taut wire has an

stodd9503

12.01.2022

(a). The value of A, k and ω is $2\times10^{-4}\ m$ , 16.02 rad/m and 3141.59 rad/s.

(b). The tension in the wire is 157.5 N.

Explanation:

Given that,

Amplitude = 0.200 mm

Frequency = 500 Hz

Speed = 196 m/s

Mass per unit length = 4.10 g/m

Suppose we need to calculate the parameters A, k, and ω.

The equation given by

$y=A\sin(kx-\omega t)$

(a). We need to calculate the amplitude

Using formula of amplitude

$A=0.200\times10^{-3}\ m$

$A=2\times10^{-4}\ m$

We need to calculate the angular frequency

Using formula of angular frequency

$\omega=2\pi f$

$\omega=2\times\pi\times500$

$\omega=3141.59\ rad/sec$

We need to calculate the angular wave number

Using formula of angular wave number

$k=\dfrac{\omega}{v}$

Put the value into the formula

$k=\dfrac{3141.59}{196}$

$k=16.02\ rad/min$

(b). We need to calculate the tension in the wire

Using formula of tension in the wire

$T=v^2\times\mu$

Put the value into the formula

$T=196^2\times4.10\times10^{-3}$

$T=157.5\ N$

Hence, (a). The value of A, k and ω is $2\times10^{-4}\ m$ , 16.02 rad/m and 3141.59 rad/s.

(b). The tension in the wire is 157.5 N.

0,0(0 оценок)