A travelling wave is partly reflected and par | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The intensity $I$ of a travelling wave is given by $I = \frac{1}{2} \rho \omega^2 A^2 v$,where $\rho$ is the density of the medium,$\omega$ is the

Vedclass · Accepted Answer

$\frac{I_i}{I_r} = \left( \frac{a_i}{a_r} \right)^2$

Vedclass · Answer

(A) The intensity $I$ of a travelling wave is given by $I = \frac{1}{2} \rho \omega^2 A^2 v$,where $\rho$ is the density of the medium,$\omega$ is the angular frequency,$A$ is the amplitude,and $v$ is the wave speed.For the incident and reflected waves,they travel in the same medium,so $\rho$,$\omega$,and $v$ are identical for both. Thus,the ratio of intensities is proportional to the square of the ratio of amplitudes: $\frac{I_i}{I_r} = \frac{\frac{1}{2} \rho \omega^2 a_i^2 v}{\frac{1}{2} \rho \omega^2 a_r^2 v} = \left( \frac{a_i}{a_r} \right)^2$.Since the transmitted wave travels into a different medium,the density $\rho$ and wave speed $v$ change,meaning the relationship between $I_t$ and $a_t$ involves different constants compared to the incident wave. Therefore,only the ratio involving the incident and reflected waves in the same medium holds as $\frac{I_i}{I_r} = \left( \frac{a_i}{a_r} \right)^2$.

$A$ travelling wave is partly reflected and partly transmitted from a rigid boundary. Let $a_i, a_r$ and $a_t$ be the amplitudes of the incident wave,reflected wave,and transmitted wave,and $I_i, I_r$ and $I_t$ be the corresponding intensities. Choose the correct alternative.

Similar Questions

$A$ person speaking normally produces a sound intensity of $40 \ dB$ at a distance of $1 \ m$. If the threshold intensity for reasonable audibility is $20 \ dB$,the maximum distance at which he can be heard clearly is ... $m$.

If the pressure amplitude in a sound wave is tripled,then the intensity of sound is increased by a factor of

The intensity of sound after passing through a slab decreases by $30\%$. On passing through two such slabs,the intensity will decrease by ..... $\%$

If the ratio of the amplitudes of two waves is $2:1$,then the ratio of their maximum and minimum intensity is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module