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  • Plane simple harmonic progressive waves of wavelengths 120cm and speed 34800cm/sec are incident normally on a plane surface which is a perfect reflection of sound. The ratio of amplitudes of vibrat

Plane simple harmonic progressive waves of wavelengths 120cm and speed 34800cm/sec are incident normally on a plane surface which is a perfect reflection of sound. The ratio of amplitudes of vibrations at points distant i) 10cm ii) 30cm from the reflection is 

Option: 1

1: 2


Option: 2

1: 0


Option: 3

1: 1


Option: 4

1: 4


Answers (1)

best_answer

y_i=a \sin \frac{2 \pi}{\lambda }(v t-x)

y_r=-a \sin \frac{2 \pi}{\lambda}(v t+x)

y=y_i+y_r=-2 a \sin \frac{2 \pi x}{\lambda} \cos \frac{2 \pi v t}{\lambda}

Amplitude (A) = -2 a \sin \frac{2 \pi x}{\lambda}

A^{\prime}=-2 a \sin \left(2 \pi \cdot \frac{10}{120}\right)=-2 a \sin \frac{2 \pi}{12}=-a

When x = 30cm, then 

A^{\prime \prime}=-2 a \sin \left(2 \pi \cdot \frac{30}{120}\right)=-2 a

\frac{A^{\prime}}{A^{\prime \prime}}=\frac{-a}{-2a}=\frac{1}{2}=1: 2

 

Posted by

Deependra Verma

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