The resultant amplitude due to superposition of two waves $y_1 = 5\,\,sin (wt - kx)$ and $y_2 = -5 \,\,cos (wt - kx - 150^o)$
Medium
Download our app for free and get started
$y_{1}=5 \sin (\omega t-k x)$
$y_{2}=-5 \cos \left(\omega t-k x-150^{\circ}\right)$
$y_{1}+y_{2}=5\left(\sin (\omega t-k x)-\sin \left(\omega t-k x-60^{\circ}\right)\right)$
$=10\left(\sin 30^{\circ} \cos \left(\omega t-k x-30^{\circ}\right)\right)$
$=5 \cos \left(\omega t-k x-30^{\circ}\right)$
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 narrow tube is bent in the form of a circle of radius $R,$ as shown in the figure. Two small holes $S$ and $D$ are made in the tube at the positions right angle to each other. A source placed at $S$ generated a wave of intensity $I_0$ which is equally divided into two parts : One part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point $D$ where a detector is placed If the minima is formed at the detector then, the magnitude of wavelength $\lambda$ of the wave produced is given byView Solution
- 2A source of sound gives five beats per second when sounded with another source of frequency $100\,{s^{ - 1}}$. The second harmonic of the source together with a source of frequency $205\,{s^{ - 1}}$ gives five beats per second. What is the frequency of the source .... ${s^{ - 1}}$View Solution
- 3View SolutionWhich of the following statements is false
- 4View SolutionA transverse wave is travelling along a string from left to right. The adjoining figure represents the shape of the string at a given instant. At this instant, among the following, choose the wrong statement.
- 5A steel wire has a length of $12.0 \;m$ and a mass of $2.10 \;kg .$ What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at $20\,^{\circ} C =343\; m s ^{-1}$View Solution
- 6A string fixed at one end is vibrating in its second overtone. The length of the string is $10\ cm$ and maximum amplitude of vibration of particles of the string is $2\ mm$ . Then the amplitude of the particle at $9\ cm$ from the open end isView Solution
- 7A closed pipe of length $10 \,cm$ has its fundamental frequency half that of the second overtone of an open pipe. The length of the open pipe ......... $cm$View Solution
- 8A trianguler pulse moving at $2\ cm/s$ on a rope approches an end at which it is free to slide on vertical pole. What is the particle speed at the free end at $\frac{3}{4}\ sec$ from the instant shown ...... $cm/s$View Solution
- 9The particle displacement of a travelling longitudional wave is represented by $\xi = \xi (x,t)$. The midpoints of a compression zone and an adjacent rarefaction zone are represented by the letter ‘$C’$ and $‘R’$. Which of the following is true?View Solution
- 10Figure shows a snapshot for a travelling sine wave along a string. Four elemental portions $a, b, c$ and $d$ are indicated on the string. The elemental portion which has maximum potential energy is/areView Solution
