Advertisements
Advertisements
Question
The equation of a simple harmonic progressive wave travelling on a string is y = 8 sin (0.02x - 4t) cm. The speed of the wave is ______.
Options
10 cm/s
20 cm/s
100 cm/s
200 cm/s
Advertisements
Solution
The equation of a simple harmonic progressive wave travelling on a string is y = 8 sin (0.02x - 4t) cm. The speed of the wave is 200 cm/s.
Explanation:
y = 8 sin (0.02x - 4t)
y = A sin `((2pix)/lambda - 2pi"nt")`
We know that,
`therefore (2pi)/lambda = 0.02`
`therefore lambda = (2pi)/0.02`
= 100 π
And 2πn = 4
`therefore "n" = 2/pi`
∴ v = nλ
`= 2/pi xx 100 pi`
= 200 cm/s.
APPEARS IN
RELATED QUESTIONS
Answer in brief:
State the characteristics of stationary waves.
Answer in brief.
For a stationary wave set up in a string having both ends fixed, what is the ratio of the fundamental frequency to the second harmonic?
Derive an expression for the equation of stationary wave on a stretched string.
A standing wave is produced in a tube open at both ends. The fundamental frequency is 300 Hz. What is the length of the tube? (speed of the sound = 340 m s-1).
What are stationary waves? Why are they called stationary waves?
Show that the distance between two successive nodes or antinodes is λ/2.
Two parallel SHMs have equations y1 = a1 sin(ωt + 2π) and y2 = a2 sin(ωt + 4π). The amplitude of the resultant is ______
When a simple harmonic progressive wave is travelling through a medium, then each succeeding particle ______
A stretched string fixed at both ends has 'rrl nodes, then the length of the string will be ______.
A glass tube is open at both ends. A tuning fork of frequency f resonates with the air column inside the tube. Now the tube is placed vertically inside water so that half the length of the tube is filled with water. Now that air column inside the tube is in unison with another fork of frequency f, ____________.
A simple harmonic progressive wave is represented as y = 0.03 sin π(2t - 0.01x) m. At a given instant of time, the phase difference between two particles 25 m apart is ______.
Find the wrong statement from the following about the equation of stationary wave given by Y = 0.04 cos(πx) sin(50 πt) m where t is in second. Then for the stationary wave.
For the stationary wave,
y = 8sin(6.25πx) cos(96πt) metre, the distance between a node and the next antinode is ____________.
For stationary waves in the medium, ____________.
The equation of a stationary wave is given by 2 sin `((pi"x")/15) "cos" (48 pi"t").`The distance between a node and its next antinode is ____________.
The wave described by y = 0.35 sin (27πt - 10πx), where x and y are in metre and tin second, is a wave travelling along the ______.
In Melde's experiment, when the wire is stretched by an empty pan, four loops are obtained and when a six-gram weight is added to the pan, the number of loops becomes one. The mass of pan is ______
The correct statement about stationary waves is that ______
In a stationary wave all particles ______
What is a stationary wave?
A closed organ pipe (closed at one end) is excited to support the third overtone. It is found that air in the pipe has ______.
A string 120 cm long is fixed at one end. The other end is moved up and down with frequency 20 Hz. On a stationary wave 4 loops are formed. The speed of the progressive wave which moves along the string is ______.
