When a wave travels in a medium, particle displacement is given by : y = asin, 2 π ,(bt -cx) ,

English

Gujarati

Hindi

14.Waves and Sound

normal

When a wave travels in a medium, the particle displacement is given by : $y = asin\, 2 \pi \,(bt -cx)$, where $a, b$ and $c$ are constants. The maximum particle velocity will be twice the wave velocity if

A

$c = \frac{1}{\pi a}$

B

$c = \pi a$

C

$b = ac$

D

$b = \frac{1}{ac}$

Solution

For the wave $A \sin (\omega t-k x),$ wave velocity is $\frac{\omega}{k}$ and maximum particle velocity is $\omega A$

Therefore:

For the given wave, the wave speed is given by, $v_{w}=\frac{b}{c}$

And the maximum particle speed is given by: $v_{p}=2 \pi a b$ So, $v_{p}=2 v_{w}$

$\Rightarrow c=\frac{1}{\pi a}$

Standard 11

Physics

Share

Similar Questions

A train approaching a railway plateform with a speed of $20\,\,m\,s^{-1}$ starts blowing the whistle speed of sound in air is $340\,\,ms^{-1}.$ If frequency of the emitted sound from the whistle is $640\,\,Hz,$ the frequency of sound as heard by person standing on the platform is …. $Hz$

normal

The displacement of an elastic wave is given by the function : $y = 3\, sin\,\omega t + 4\, cos\,\omega t$ where $y$ is in $cm$ and $t$ is in $s$. The resultant amplitude is …… $cm$

normal

A train whistling at constant frequency is moving towards a station at a constant speed $V$. The train goes past a stationary observer on the station. The frequency $n'$ of the sound as heard by the observer is plotted as a function of time $t (Fig.)$ . Identify the expected curve

normal

A point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at a distance of $9\ meters$ and $25\ meters$ respectively from the source. The ratio of the amplitudes of the waves at $P$ and $Q$ is

normal

An organ pipe $P_1$ closed at one end vibrating in its first overtone. Another pipe $P_2$ open at both ends is vibrating in its third overtone. They are in a resonance with a given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is

normal