Advertisements
Advertisements
प्रश्न
The equation of simple harmonic progressive wave is, y = sin π/2 (4t/0.025 – x/0.25). Where all quantities are in the S.I. system. Find the amplitude, frequency, wavelength, and velocity of the wave.
Advertisements
उत्तर
- Given equation:
y = sin`pi/2((4"t")/0.025 - "x"/0.25)`
y = sin`((2pi"t")/0.025 - (pi"x")/0.5)`
Comparing above equation with y = A sin`(ω"t" - (2pi"x")/λ)`
∴ A = 1 m - ω = `(2pi)/0.025`
∴ 2πn = `(2pi)/0.025`
∴ n = 40 Hz - `(2pi)/λ = pi/0.5`
∴ λ = 1 m - v = nλ
= 40 × 1
= 40 m/s
The amplitude, frequency, wavelength, and velocity of the wave are 1 m, 40 Hz, 1 m, and 40 m/s respectively.
APPEARS IN
संबंधित प्रश्न
The equation of a simple harmonic progressive wave is given by, y = 5cosπ`[200t - x/150]`, where x and y are in cm and ‘t’ is in second. Then the velocity of the wave is ______.
Two open pipes of different lengths and same diameter in which the air column vibrates with fundamental frequencies 'n1', and 'n2' respectively. When both pipes are joined to form a single pipe, its fundamental frequency will be ______.
A tube closed at one end and containing air produces fundamental note of frequency 256 Hz. If the tube is open at both ends, the fundamental frequency will be ____________.
If length of a closed organ pipe is 60 cm and velocity of sound is 360 m/s, then the frequency of 1st overtone is ____________.
An air column, closed at one end and open at the other resonates with a tuning fork of frequency v, when its length is 45 cm, 99 cm and at two other lengths in between these values. The wavelength of sound in air column is ____________.
An open organ pipe produces its fundamental frequency f. When the pipe is dipped in water so that `2/5` of its length is under water, then its 5 fundamental frequency becomes ____________.
A pipe closed at one end produces a fundamental note of 412 Hz. It is cut into two pieces of equal length. The fundamental notes produced by the two pieces are ____________
An open pipe of certain length produces fundamental frequency f1. A closed pipe of some other length produces fundamental .frequency f2. When the two are joined to form a longer close tube, its fundamental frequency will be ____________.
Transverse waves of the same frequency are generated in two steel wires A and B. The diameter of A is twice that of B and the tension in A is half that in B. The ratio of the velocities of waves in A and B is ____________.
A transverse wave propagating along the string is y = 0.3 sin (x + 20t) where x, y are in metre and t in second. The linear density of the string is 1.2 x 10-4 kg/m. The tension in the string is ______.
A stretched uniform wire of length L under tension T is vibrating with frequency 'n' . A closed pipe of same length is also vibrating with same fundamental frequency 'n'. If T is increased by 16 N, it is in resonance with 2nd harmonic of same closed pipe. The initial tension in the wire is ______.
An organ pipe has fundamental frequency 100 Hz. If its one end is closed, the frequencies produced will be ______.
A tuning fork with frequency 800 Hz produces resonance in a resonance column tube with upper end open and lower end closed by water surface. Successive resonances are observed at lengths 9.75 cm, 31.25 cm and 52.75 cm. The speed of sound in air is, ____________.
The equation of stationary wave on a string clamped at both ends and vibrating in the third harmonic is given by y = 0.5 sin (0.314 x) cos (600 πt), where x and y are in cm and t in second. The length of the vibrating string is ______
(π = 3.14)
The air column in an organ pipe closed at one end is made to vibrate so that there are 2 nodes and antinodes each. The mode of vibration is called ______
When source of sound moves towards a stationary observer, the wavelength of sound received by him ______.
The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produce three beats. The length of open pipe is made `1/3` rd and closed pipe is made three times the original, the number of beats produced will be ______.
Two uniform wires of the same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and radius of the first wire is the twice the radius of the second wire, then the ratio of the lengths of the first wire to second wire is ______.
An open pipe is in resonance in its 2nd harmonic with tuning fork of frequency f1. Now, it is closed at one end. If the frequency of the tuning fork is increased slowly from f1, then again a resonance is obtained with a frequency f2. If in this case the pipe vibrates nth harmonic, then ______.
An organ pipe closed at one end resonates with a tuning fork of frequencies 180 Hz and 300 Hz. It will also resonate with tuning fork of frequency ______.
Explain why velocity increases when water flowing in a broad pipe enters a narrower pipe. A sonometer wire, 36 cm long, vibrates with a frequency of 288 Hz in the fundamental mode when it is under a tension of 24.5 N. Calculate the linear density of the material of the wire
A stretched string 0.7 m long and fixed at its ends vibrates in the second overtone of frequency 300 Hz. Find the speed of the transverse wave on the string.
How does the fundamental frequency of a vibrating string depend on the radius of the cross-section of the string and the mass density material of the string?
Two consecutive harmonics of air column in a pipe closed at one end are frequencies 150 Hz and 250 Hz. Calculate the fundamental frequency.
Two organ pipe, open at both ends, are sounded together and 5 beats are heard per second. The length of shorter pipe is 0.25 m. Find the length of the other pipe. (Given: Velocity of sound in air = 350 m/s and end correction at one end = 0.015 m, same for both pipes.)
A wire of length L, diameter 'd' density of material 'e' is under tension 'T', having fundamental frequency of vibration nA. Another wire of length 2L, tension 2T, density 2e and diameter 3d has fundamental frequency of vibration nB. The ratio nB: NA is ______.
