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Waves — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsWaves5 Marks
Question
A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45Hz. The mass of the wire is 3.5 × 10–2kg and its linear mass density is 4.0 × 10–2kg m–1. What is
  1. The speed of a transverse wave on the string,
  2. The tension in the string?
✓

Answer

  1. Mass of the wire, m = 3.5 × 10–2kg

Linear mass density, $\mu=\frac{\text{m}}{\text{l}}=4.0\times10^2\text{kg m}^{-1}$

Frequency of vibration, v = 45Hz

$\therefore$ length of the wire, $\text{l}=\frac{\text{m}}{\mu}=\frac{3.5\times10^{-2}}{4. 0\times10^{-2}}=0.875\text{m}$

The wavelength of the stationary wave $(\lambda)$ is related to the length of the wire by the relation:

$\lambda=\frac{2\text{l}}{\text{m}}$

where,

n = Number of nodes in the wire

For fundamental node, n = 1:

$\lambda=2\text{l}$

$\lambda=2\times0.875=1.75\text{m}$

The speed of the transverse wave in the string is given as:

$\text{v}=\text{v}\lambda=45\times1.75=78.75\text{m/s}$

  1. The tension produced in the string is given by the relation:

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

$=(78.75)^2\times4.0\times10^{-2}=248.06\text{N}$

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