Physics - Wave on String Question with Solution | TestHub

PhysicsWave on StringVelocityMedium3 minQB

PhysicsMediumnumerical

Passage / Comprehension

A string of length $L$ is fixed at one end and under tension due to a mass $M = 25$ kg hanging from the other end, as shown in the sketch. Coordinate axes are chosen so that the string runs from $x = - \frac{L}{2}$ to $x = \frac{L}{2}$ , and $y$ is the transverse displacement. The string is vibrating at one of its resonant frequencies with displacement $y (x, t) = 0.05 cos (12.0 x) sin (360 t)$ .

If the mass density of the string is $μ$ , then what is the value of the inverse of $μ$ ?

Answer:

3.60

Solution:

Wave speed:
$v = \frac{ω}{k} = \frac{360}{12} = 30$ m/s $= \frac{T}{μ}$
$T = M g = 250$ N (g = 10 m/s $^{2}$ )
$μ = \frac{T}{v ^{2}} = \frac{250}{900} = \frac{5}{18}$
$\frac{1}{μ} = 3.6$
Printed key: 3.60.

Subject:PhysicsTopic:Wave on StringSubtopic:Velocity

⏱ 3mℹ️ Source: QB

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