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Wave Motion and Waves on a String — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsWave Motion and Waves on a String3 Marks
Question
A $660Hz$ tuning fork sets up vibration in a string clamped at both ends. The wave speed for a transverse wave on this string is $220m/s$ and the string vibrates in three loops.
  1. Find the length of the string.
  2. If the maximum amplitude of a particle is $0.5\ cm,$ write a suitable equation describing the motion.
✓

Answer

Frequency of the tuning fork, $\text{f}=660\text{Hz}$ Wave speed, $\text{v}=220\text{ms}$
$\Rightarrow\lambda=\frac{\text{v}}{\text{f}}=\frac{1}{3}\text{m}$
No.of loops $= 3$
  1. So, $\text{f}=\Big(\frac{3}{2\text{l}}\Big)\text{v}$
$\Rightarrow\text{l}=50\text{cm}$
  1. The equation of resultant stationary wave is given by
$\text{y}=2\text{A}\cos\Big(\frac{2\pi\text{x}}{\text{Ql}}\Big)\sin\Big(\frac{2\pi\text{vt}}{\lambda}\Big)$
$\Rightarrow\text{y}(0.5\text{cm})\cos(0.06\pi\text{cm}^{-1})\sin(1320\pi\text{s}^{-1})$

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