Two points are located at a distance of $10\; m$ and $15 \;m$ from the source of oscillation. The period of oscillation is $0.05 \;sec$ and the velocity of the wave is $300 \;m / s$. What is the phase difference between the oscillations of two points?
AIPMT 2008, Medium
Download our app for free and get started
Given:- Two points are located at a distance of $10\,m$ and $15\,m$
The period of oscillation $=0.05\,s$
The velocity of the wave $=300\,m / s$
To find:- The phase difference between the oscillation of two points.
Solution:- We know that,
Path difference $=\frac{2 \pi}{\lambda} \times$ path difference
Path difference between two points,
$\Delta x =15-10=5\,m$
Time period, $T =0.5^{ s }$
$\Rightarrow$ frequency $v =\frac{1}{ T }=\frac{1}{0.05}=20\,Hz$
Velocity $v =300\,m / s$
$\therefore$ Wavelenght $\lambda=\frac{ v }{ n }=\frac{300}{20}=15\,m$
Hence, phase difference
$\Delta \phi=\frac{2 \pi}{\lambda} \times x =\frac{2 \pi}{15} \times 5=\frac{2 \pi}{3}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A car sounding a horn of frequency $ 1000 Hz$ passes an observer. The ratio of frequencies of the horn noted by the observer before and after passing of the car is $11 : 9$. If the speed of sound is v, the speed of the car isView Solution
- 2View SolutionWhich of the following statements are wrong about the velocity of sound in air:
- 3$Assertion :$ A transverse waves are produced in a very long string fixed at one end. Only progressive wave is observed near the free end.View Solution
$Reason :$ Energy of reflected wave does not reach the free end. - 4Two sound waves (expressed in $CGS$ units) given by ${y_1} = 0.3\sin \frac{{2\pi }}{\lambda }(vt - x)$ and ${y_2} = 0.4\sin \frac{{2\pi }}{\lambda }(vt - x + \theta )$ interfere. The resultant amplitude at a place where phase difference is $\pi /2$ will be .... $ cm$View Solution
- 5The vibration of a string fixed at both ends are described by $Y= 2 \,\,sin(\pi x) \,\,sin\,\,(100\pi t)$ where $Y$ is in $mm$,$x$ is in $cm$,$t$ in $sec$ thenView Solution
- 6View SolutionQuality of a musical note depends on
- 7Suppose that the speed of sound in air at a given temperature is $400 m/sec$. An engine blows a whistle at $1200 Hz$ frequency. It is approaching an observer at the speed of $100 m/sec$. What is the apparent frequency as heard by the observer .... $Hz$View Solution
- 8A sonometer wire, with a suspended mass of $M = 1\, kg$, is in resonance with a given tuning fork. The apparatus is taken to the moon where the acceleration due to gravity is $(1/6)$ that on earth. To obtain resonance on the moon, the value of $M$ should be ......... $kg$View Solution
- 9In a resonance tube the first resonance with a tuning fork occurs at $16 cm$ and second at $49 cm.$ If the velocity of sound is $330 m/s,$ the frequency of tuning fork isView Solution
- 10$Assertion :$ The pitch of wind instruments rises and that of string instruments falls as an orchestra warms up.View Solution
$Reason :$ When temperature rises, speed of sound increases but speed of wave in a string fixed at both ends decreases.