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
A pipe closed at one end can produce overtones at frequencies 640 Hz, 896 Hz, and 1152 Hz. Calculate the fundamental frequency.
An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of length of open pipe to that of closed pipe is ______.
When open pipe is closed from one end third overtone of closed pipe is higher in frequency by 150 Hz, then second overtone of open pipe. The fundamental frequency of open end pipe will be ____________.
The fundamental frequency of a closed pipe is 400 Hz. If `1/3`rd pipe !s tilled with water, then the 3 frequency of 2nd harmonic of the pipe will be (neglect and correction).
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 ______.
In a fundamental mode the time required for the sound wave to reach upto the closed end of a pipe filled with air is 't' second. The frequency of vibration of air column is ________.
A thin wire of 99 cm is fixed at both ends as shown in figure. The wire is kept under a tension and is divided into three segments of lengths l1, l2, and l3 as shown in figure. When the wire is made to vibrate respectively with their fundamental frequencies in the ratio 1:2:3. Then the lengths l1, l2, and l3 of the segments respectively are (in cm).
Two strings A and B of same material are stretched by same tension. The radius of the string A is double the radius of string B. Transverse wave travels on string A with speed 'VA' and on string B with speed 'VB'. The ratio `"V"_"A"/"V"_"B"` 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 ____________.
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 ______.
An organ pipe has fundamental frequency 100 Hz. If its one end is closed, the frequencies produced will be ______.
A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air colunm in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.
If we study the vibration of a pipe open at both ends, then which of the following statements is not true?
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)
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 ______.
The fundamental frequency of an air column is a pipe closed at one end is 100 Hz. If the same pipe is open at both the ends, the frequencies produced in Hz are ______.
If the end correction of an open pipe is 0.8 cm, then the inner radius of that pipe will be ______.
A pipe Pc closed at one end and point Po open at both ends are vibrating in the second overtone. They are in resonance with a given tuning fork. The ratio of the length of pipe Pc to that of pipe, Po is ______.
(Neglect end correction).
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 ______.
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.
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.)
There are two organ pipes of the same length and the same material but of different radii. When they are emitting fundamental notes.
Two uniform strings ‘A’ and ‘B’ made of steel are made to vibrate under same tension. If the first overtone of ‘A’ is equal to second overtone of ‘B’ and radius of ‘A’ is twice that of ‘B’. Then the ratio of length of string ‘A’ to that of ‘B’ is ______.
