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.
Find the amplitude of the resultant wave produced due to interference of two waves given as y1 = A1 sinωt, y2 = A2 sin(ωt + φ)
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?
For a stationary wave set up in a string having both ends fixed, what is the ratio of the fundamental frequency to the third harmonic?
When a simple harmonic progressive wave is travelling through a medium, then each succeeding particle ______
The equation of simple harmonic progressive wave is given by Y = a sin 2π (bt - cx). The maximum particle velocity will be twice the wave velocity if ______.
Two travelling waves, y1 = A sin [k (x + ct)] and y2 = A sin [k (x - ct)] are superposed on a string. The distance between adjacent nodes is ____________.
A stretched string fixed at both ends has 'rrl nodes, then the length of the string will be ______.
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 ______.
A stretched string of 1 m length and mass 5 x 10-4 kg is having tension of 20 N. If it is plucked at 25 cm from one end then it will vibrate with frequency ____________.
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, ____________.
lf the length of a stretched string is shortened by 40 % and the tension is increased by 44%, then the ratio of the final and initial fundamental frequencies are ____________.
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 ______
What is a stationary wave?
