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Tems11 [23]
3 years ago
5

A string is stretched to a length of 376 cm and

Physics
1 answer:
sergey [27]3 years ago
7 0

Answer: 53.09Hz

Explanation:

The fundamental frequency of an ideal taut string is:

Fn= n/2L(√T/μ)

Where:

F= frequency per second (Hz)

T= Tension of the string (cm/s sqr)

L= Length of the string (cm)

μ= Linear density or mass per unit length of the string in cm/gm

√T/μ= square root of T divided by μ

It is important to note:

Note: Typically, tension would be in newtons, length in meters and linear density in kg/m, but those units are inconvenient for calculations with strings. Here, the smaller units are used.

F1= 1/2(376cm)(0.01/1) × (√574/(0.036g/cm)(0.1kg/m÷1g/cm)

F1= 0.1329 × 399.30

= 53.09Hz

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Answer:

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Explanation:

From the question we are told that

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        The  rate  is  v =  0.5*10^{-9} \ m^3 /t

       The viscosity is  \eta  =  \frac{\pi}{8} * \frac{P *  r^4}{v}

The error in the viscosity is mathematically represented  as

       \Delta  \eta  = | \frac{\delta \eta}{\delta P}| *  \Delta  P   +    |\frac{\delta \eta}{\delta r} |*  \Delta  r +  |\frac{\delta \eta}{\delta v} |*  \Delta  v

   Where  \frac{\delta \eta }{\delta P} =  \frac{\pi}{8} *  \frac{r^4}{v}

and         \frac{\delta \eta }{\delta r} =  \frac{\pi}{8} *  \frac{4* Pr^3}{v}

and          \frac{\delta \eta }{\delta v} =  - \frac{\pi}{8} *  \frac{Pr^4}{v^2}

So  

             \Delta  \eta  = \frac{\pi}{8} [ |\frac{r^4}{v}  | *  \Delta  P   +    | \frac{4 *  P * r^3}{v}  |*  \Delta  r +  |-\frac{P* r^4}{v^2}  |*  \Delta  v]

substituting values

            \Delta  \eta  = \frac{\pi}{8} [ |\frac{(0.002)^4}{0.5*10^{-9}}  | *  1750   +    | \frac{4 *  4 *10^{5} * (0.002)^3}{0.5*10^{-9}}  |*  0.0002 +  |-\frac{ 4*10^{5}* (0.002)^4}{(0.5*10^{-9})^2}  |*  0 ]

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