Question

A particle on a stretched string supporting a travelling wave, takes 5⋅0 ms to move from its mean position to the extreme position. The distance between two consecutive particles, which are at their mean positions, is 2⋅0 cm. Find the frequency, the wavelength and the wave speed.

Answer 1

Time taken to reach from the mean position to the extreme position,
\[\frac{T}{4}\]  = 5 ms
Time period (T) of the wave:

\[T = 4 \times 5  ms\] 

\[     = 20 \times  {10}^{- 3}  = 2 \times  {10}^{- 2}   s\] 

Wavelength (λ) = \[2 \text{ times Distance  between  two  mean  positions}\] \[= 2 \times 2  cm = 4  cm\]

\[Frequency,   f = \frac{1}{T}\] 

\[                                         = \frac{1}{\left( 2 \times {10}^{- 2} \right)}\] 

\[                                         = 50  Hz\] 

\[ \text{Wave  speed },   v =   [\lambda f\] 

\[                                             = 4 \times  {10}^{- 2}  \times 50\] 

\[                                             = 200 \times  {10}^{- 2} \] 

\[                                             = 2  m/s\]