Physics, 17.07.2020 23:01, mommer2019

A piano wire has a linear mass density of μ = 4.85 ✕ 10−3 kg/m. Under what tension (in N) must the string be kept to produce waves with a wave speed of 595.00 m/s?

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answered: thisbegaby

The string must have a tension of 1717.021 newtons to have a wave speed of 595 meters per second.

Explanation:

This is a case where transversal waves occur. The formula of speed for transversal waves is:

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

Where:

- Speed of the transversal wave, measured in meters per second.

$\mu$ - Linear mass density, measured in kilograms per meter.

- Tension, measured in newtons.

The tension is now cleared:

$T = v^{2}\cdot \mu$

If $v = 595\,\frac{m}{s}$ and $\mu = 4.85\times 10^{-3}\,\frac{kg}{m}$ , the tension needed is:

$T = \left(595\,\frac{m}{s} \right)^{2}\cdot \left(4.85\times 10^{-3}\,\frac{kg}{m} \right)$

$T = 1717.021\,N$

The string must have a tension of 1717.021 newtons to have a wave speed of 595 meters per second.

answered: Guest

f=ma newton's second law 7x8=56n

answered: Guest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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A piano wire has a linear mass density of μ = 4.85 ✕ 10−3 kg/m. Under what tension (in N) must the s...