Two waves are propagating to the point $P$ along a straight line produced by two sources $A$ and $B$ of simple harmonic and of equal frequency. The amplitude of every wave at $P$ is $‘a’$ and the phase of $A$ is ahead by $\frac{\pi }{3}$ than that of $B$ and the distance $AP$ is greater than $BP$ by $50 cm.$ Then the resultant amplitude at the point $P$ will be, if the wavelength is $1$ meter
Medium
Download our app for free and get started
(d) Path difference $(\Delta x)$ $ = 50\,cm\, = \frac{1}{2}m$
$\therefore $ Phase difference $\Delta \phi = \frac{{2\pi }}{\lambda } \times $$\Delta x $
$\Rightarrow \phi = \frac{{2\pi }}{1} \times \frac{1}{2} = \pi $
Total phase difference = $\pi - \frac{\pi }{3} = \frac{{2\pi }}{3}$
==> $A = \sqrt {{a^2} + {a^2} + 2{a^2}\cos (2\pi /3)} = a$
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
- 1The ratio of maximum to minimum intensity due to superposition of two waves is $\frac{{49}}{9}$ Then the ratio of the intensity of component waves is .View Solution
- 2A uniform tube of length $60.5\,cm$ is held vertically with its lower end dipped in water. A sound source of frequency $500\,Hz$ sends sound waves into the tube. When the length of tube above water is $16\,cm$ and again when it is $50\,cm,$ the tube resonates with the source of sound. Two lowest frequencies (in $Hz$), to which tube will resonate when it is taken out of water, are (approximately).View Solution
- 3The equation of a wave travelling on a string is $y = 4\sin \frac{\pi }{2}\left( {8t - \frac{x}{8}} \right)$. If $x$ and $y$ are in $cm,$ then velocity of wave isView Solution
- 4A source of sound of frequency $600 Hz$ is placed inside water. The speed of sound in water is $1500 m/s$ and in air is $300 m/s.$ The frequency of sound recorded by an observer who is standing in air is .... $Hz$View Solution
- 5An open pipe of length $33 cm$ resonates with frequency of $100 Hz$. If the speed of sound is $330 m/s$, then this frequency isView Solution
- 6View SolutionThe ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is
- 7Which of the following is $CORRECT$View Solution
- 8View SolutionWhich of the following is different from others
- 9The length of the wire shown in figure between the pulleys is $1.5\, m$ and its mass is $12.0\,g$. The frequency of vibration with which the wire vibrates in three loops forming antinode at the mid point of the wire is $(g = 9.8 \,m/s^2)$View Solution
- 10If the speed of the wave shown in the figure is $330m/s$ in the given medium, then the equation of the wave propagating in the positive $x-$direction will be (all quantities are in $M.K.S.$ units)View Solution
