Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
Advertisement Remove all ads

The Equation of a Travelling Sound Wave is Y = 6.0 Sin (600 T − 1.8 X) Where Y is Measured in 10−5 M, T in Second and X in Metre. (A) Find the Ratio of the Displacement - Physics

Sum

The equation of a travelling sound wave is y = 6.0 sin (600 t − 1.8 x) where y is measured in 10−5 m, t in second and x in metre. (a) Find the ratio of the displacement amplitude of the particles to the wavelength of the wave. (b) Find the ratio of the velocity amplitude of the particles to the wave speed.

Advertisement Remove all ads

Solution

Given:
Equation of a travelling sound wave is y = 6.0 sin (600 t − 1.8 x),
where y is measured in 10−5 m,
t in second,
x in metre.
Comparing the given equation with the wave equation, we find:
Amplitude  A = 6 \[\times\]10-5 m

\[(a) \text{ We  have: } \] 

\[  \frac{2\pi}{\lambda} = 1 . 8  \] 

\[ \Rightarrow \lambda = \left( \frac{2\pi}{1 . 8} \right)\] 

\[\text { So,   required  ratio: } \] 

\[  \frac{A}{\lambda} = \frac{6 . 0 \times (1 . 8) \times {10}^{- 5} m/s}{(2\pi)} = 1 . 7 \times  {10}^{- 5}   m\]

(b) Let Vy be the velocity amplitude of the wave.

\[\text { Velocity  v }= \frac{dy}{dt}\] 

\[v = \frac{d\left[ 6  \sin  \left( 600  t - 1 . 8  x \right) \right]}{dt}\] 

\[ \Rightarrow v = 3600  \cos  (600t - 1 . 8x) \times  {10}^{- 5}   m/s\] 

\[\text { Amplitute }  V_y  = 3600 \times  {10}^{- 5} m/s\] 

\[\text { Wavelength: }\] 

\[  \lambda = \frac{2\pi}{1 . 8}\] 

\[\text { Time  period: } \] 

\[T = \frac{2\pi}{\omega}\] 

\[ \Rightarrow   T = \frac{2\pi}{600}\] 

\[\text { Wave  speed  v } = \frac{\lambda}{T}\] 

\[ \Rightarrow v = \frac{600}{1 . 8} = \frac{100}{3}  m/s\] 

\[\text { Required  ratio: } \] 

\[\left( \frac{V_y}{v} \right) = \frac{3600 \times 3 \times {10}^{- 5}}{1000} = 1 . 1 \times  {10}^{- 4}   m\]

Concept: Wave Motion
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 16 Sound Waves
Q 8 | Page 353
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×