When both source and listener are approaching each other the observed frequency of sound is given by ( $V_L$ and $V_S$ is the velocity of listener and source respectively, $n_0=$ radiated frequency)
✓
$n=n_0\left[\frac{V+V_L}{V-V_S}\right]$
B
$n=n_0\left[\frac{V-V_L}{V+V_S}\right]$
C
$n=n_0\left[\frac{V-V_L}{V-V_S}\right]$
D
$n=n_0\left[\frac{V+V_L}{V+V_S}\right]$
Answer
Correct option: A.
$n=n_0\left[\frac{V+V_L}{V-V_S}\right]$
(a) :As, both source and listener are approaching to each other. So, by Doppler's effect $ n=n_0\left(\frac{V+V_L}{V-V_S}\right) $
Sound waves of frequency $600 Hz$ fall normally on a perfectly reflecting wall. The shortest distance from the wall at which all particles will have maximum amplitude of vibration is (speed of sound $=300 m s ^{-1}$ )
A
$\frac{1}{4} m$
✓
$\frac{1}{8} m$
C
$\frac{3}{8} m$
D
$\frac{7}{8} m$
Answer
Correct option: B.
$\frac{1}{8} m$
(b) :The minimum distance of rarefaction is $\frac{\lambda}{4}$ As, $v=\lambda f$ $ \lambda=\frac{v}{f}=\frac{300}{600}=\frac{1}{2} m ; \quad d=\frac{\lambda}{4}=\frac{1}{8} m $
A source of sound is moving towards a stationary observer with $\left(\frac{1}{10}\right)^{\text {th }}$ of the speed of sound. The ratio of apparent to real frequency is
The equation of the wave is $y=10 \sin \left(\frac{2 \pi t}{30}+\alpha\right)$. If the displacement is $5 cm$ at $t=0$ then the total phase at $t=7.5 s$ will be $\left(\sin 30^{\circ}=0.5\right)$
The displacement of a wave travelling in the $x$ direction is $y=10^{-4} \sin \left[600 t-2 x+\frac{\pi}{3}\right] m$, where $x$ is in metre and $t$ in second. The speed of the wave is
✓
$300 m / s$
B
$200 m / s$
C
$150 m / s$
D
$600 m / s$
Answer
Correct option: A.
$300 m / s$
(a) :The given equation, $ y=10^{-4} \sin \left[600 t-2 x+\frac{\pi}{3}\right] m $ On comparing this equation with standard equation with standard equation, $y=A \sin (\omega t-k x)$, we get $ \begin{aligned} \omega & =600 ; k=2 \\ v & =\frac{\omega}{k}=\frac{600}{2}=300 m / s \end{aligned} $
Sound of frequency $1000 Hz$ from a stationary source is reflected from an object approaching the source at $30 m s ^{-1}$, back to a stationary observer located at the source. The speed of sound in air is $330 m s ^{-1}$. The frequency of the sound heard by the observer is
✓
$1200 Hz$
B
$1000 Hz$
C
$1090 Hz$
D
$1100 Hz$
Answer
Correct option: A.
$1200 Hz$
(a) :The frequency of sound from the stationary source reaches the object which is approaching towards the source is $ n^{\prime}=n_0\left(\frac{v+v_o}{v}\right) $ where, $n_0=$ frequency of source, $v=$ speed of sound in air and $v_o=$ speed of the object. The frequency of reflected sound from the object heard by the stationary observer located at the source is $ \begin{aligned} & n^{\prime \prime}=n^{\prime}\left(\frac{v}{v-v_o}\right)=n_0\left(\frac{v+v_o}{v-v_o}\right) \\ & =1000\left(\frac{330+30}{330-30}\right)=1200 Hz \end{aligned} $
When source of sound moves towards a stationary observer, the wavelength of sound received by him
✓
decreases while frequency increases.
B
remains the same whereas frequency increases.
C
increases and frequency also increases.
D
decreases while frequency remains the same.
Answer
Correct option: A.
decreases while frequency increases.
(a) :The apparent frequency of sound during the relative motion of source and observer is given by $ n_a=n\left[\frac{v \pm v_o}{v \mp v_s}\right] $ Since observer is at rest at $v_o=0$ $ n_a=n\left[\frac{v}{v-v_s}\right] $ So, the frequency increase, as wavelength decreases.
The observer is moving with velocity $v_0$ towards the stationary source of sound and then after crossing moves away from the source with velocity $v_0$. Assume that the medium through which the sound waves travel is at rest. If $v$ is the velocity of sound and $n$ is the frequency emitted by the source then the difference between apparent frequencies heard by the observer is
✓
$\frac{2 n v_0}{v}$
B
$\frac{n v_0}{v}$
C
$\frac{v}{2 n v_0}$
D
$\frac{v}{n v_0}$
Answer
Correct option: A.
$\frac{2 n v_0}{v}$
(a) :The frequency heard by the observer, when moving towards the stationary source $ n^{\prime}=n\left(\frac{v+v_0}{v}\right) $ The frequency heard by the observer, when moving away from the stationary source $ n^{\prime \prime}=n\left(\frac{v-v_0}{v}\right) $ The difference between apparent frequencies $=n^{\prime}-n^{\prime \prime}$ $ =\frac{n}{v}\left[v+v_0-v+v_0\right]=\frac{2 n v_0}{v} $
When the observer moves towards the stationary source with velocity, $V_1$, the apparent frequency of emitted note is $F_1$. When the observer moves away from the source with velocity $V_1$, the apparent frequency is $F_2$. If $V$ is the velocity of sound in air and $\frac{F_1}{F_2}=2$ then $\frac{V}{V_1}=$ ?
A
2
✓
3
C
4
D
5
Answer
Correct option: B.
3
(b) :When the observer moves towards the stationary source, apparent frequency of emitted note, $ F_1=\left(\frac{V+V_1}{V}\right) n ...(i) $ When the observer moves away from the stationary source, apparent frequency of emitted note $ F_2=\left(\frac{V-V_1}{V}\right) n $ ...(ii) Dividing eqn. (i) by eqn. (ii), we get $ \begin{aligned} & \frac{F_1}{F_2}=\frac{V+V_1}{V-V_1} \\ & \because \quad \frac{F_1}{F_2}=2 \text { (given) } \therefore \quad \frac{V+V_1}{V-V_1}=2 \\ & \Rightarrow \quad V+V_1=2 V-2 V_1 \Rightarrow V=3 V_1 \text { or } \frac{V}{V_1}=3 \end{aligned} $
The pitch of the whistle of an engine appears to drop to $\left(\frac{5}{6}\right)^{\text {th }}$ of original value when it passes a stationary observer. If the speed of sound in air is $350 m / s$ then the speed of engine is
A
$35 m / s$
✓
$70 m / s$
C
$105 m / s$
D
$140 m / s$
Answer
Correct option: B.
$70 m / s$
(b) :Pitch of sound depends on its frequency. Speed of sound, $v=350 m s ^{-1}$ Speed of engine, $u_s=$ ? Apparent pitch (frequency) heard by observer $=\left(\frac{5}{6}\right)^{\text {th }}$ of original pitch (frequency) of engine. Let original frequency of the engine be $v_0$. Apparent frequency heard by stationary observer $=0$ Then $v=\left(\frac{5}{6}\right) v_0$ $\because \quad$ Engine is moving away from the source $ \therefore \quad v=\left(\frac{v}{v+u_s}\right) v_0 $ So, $\frac{5}{6} v_0=\frac{350}{350+u_s} \times v_0$ $ 350+u_s=420 \therefore u_s=70 m s ^{-1} . $
A plane sound wave travelling with velocity $v$ in a medium $A$ reaches a point on the interface of medium $A$ and medium $B$. If velocity of sound in medium $B$ is $2 v$, the angle of incidence for total internal reflection of the wave will be greater than $\left(\sin 30^{\circ}=0.5\right.$ and $\left.\sin 90^{\circ}=1\right)$
A
$15^{\circ}$
✓
$30^{\circ}$
C
$45^{\circ}$
D
$90^{\circ}$
Answer
Correct option: B.
$30^{\circ}$
(b) :Let $i$ be angle of incidence and $i_c$ be the critical angle. For total internal reflection, $i>i_c$ Here, $\sin i_c=\frac{v}{2 v}=\frac{1}{2}$ or $i_c=\sin ^{-1}\left(\frac{1}{2}\right)=\sin ^{-1}(0.5)=30^{\circ} \quad \therefore \quad i>30^{\circ}$
A thunder clap was heard 6 seconds after a lightening flash was seen. If the speed of sound in air is 340 m/s at the time of observation, the distance of the listener from the thunder clap is ………………
A sound note emitted from a certain source has a velocity of 300 m/s in air and 1050 m/s in water. If the wavelength of sound note in air is 2 m, the wavelength in water is …………
Wavelength of the transverse wave is 30 cm. If the particle at some instant has displacement 2 cm, find the displacement of the particle 15 cm away at the same instant.