Physics, 08.04.2020 03:26, chrissycherry

A small steel wire of diameter 1.0 mm is connected to an oscillator and is under a tension of 7.5 N. The frequency of the oscillator is 60.0 Hz and it is observed that the amplitude of the wave on the steel wire is 0.50 cma. What is the power output of the oscillator, assuming that the wave is not reflected back?b. If the power output stays constant but the frequency is doubled, what is the amplitude of the wave?

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answered: carnations

The output power is P= 0.764Watt

The Amplitude would decrease by $\frac{1}{2}$

Explanation:

From the question we are told that

The diameter of the steel wire is = 1.0mm $= \frac{1}{1000} = 1.0*10^{-3}m$

The raduis of this steel wire is $r = \frac{1*10^{-3}}{2} = 0.5*10^{-3}m$

Now from the question we can deduce that the power output is equal to the power being transmitted by wave on the wire this is mathematically represented as

$P = \frac{1}{2} \mu w^2 A^2 v ----(1)$

Where $\mu$ is the mass per unit length of the wire

This is mathematically evaluated as

$\mu = a* \rho$

Where a is the area of the the wire = $\pi r^2 = (3.142 * 0.5*10^{-3})^2 =7.855*10^{-7}m^2$

$\rho$ is the density of steel with a generally value of 7850 kg/m^3

$\mu = 7.855*10^{-7} *7850$

$= 6.162*10^{-3}kg/m$

is velocity of the wave

This is mathematically evaluated as

$w=2 \pi f$

substituting 60Hz for f

We have

w = 2 *3.142 * 60

$=377.04 \ rad/s$

is the amplitude with a given value of 0.50 cm $= \frac{0.50}{100} = 0.50 *10^{-2}m$

v is the linear velocity of the wave

This is mathematically evaluated as

$v = \sqrt{\frac{T}{\mu} }$

Where T is the tension with a given value of 7.5N

$v = \sqrt{\frac{7.5}{6.162*10^{-3}} }$

=34.89 m/s

Substituting values into equation 1

$P = 6.162*10^{-3}* 377.04^2 * (0.5*10^{-2})^2 * 34.89$

P= 0.764Watt

Since the doubling of the frequency does not affect the amplitude and from equation one the output power is $\ \frac{1}{2}$ of the Amplitude, Then the Amplitude would decrease by $\frac{1}{2}$

answered: Guest

u can delete ur account.

1. go on google and write

2 open this and click on your profile pic and if your profile is not appearing, then u have to log in.

3. when u click on your profile pic, there appears four options on the top.

4. click on the 1st option and scroll down and go at the bottom.

5. click on edit profile.

6. there appears a option 'prefernces' and at that option at the right side , 'edit' is written.

7. click on the edit option.

8. there is a option " i want to delete my account" and click on that.

hope this u

and ur welcm

: )

answered: Guest

the bal will not change its velocity.

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A small steel wire of diameter 1.0 mm is connected to an oscillator and is under a tension of 7.5 N....