Advertisements
Advertisements
Question
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
Solution
- 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
RELATED QUESTIONS
Answer in brief:
What are harmonics and overtones?
A pipe closed at one end can produce overtones at frequencies 640 Hz, 896 Hz, and 1152 Hz. Calculate the fundamental frequency.
Find the fundamental, first overtone, and second overtone frequencies of a pipe, open at both the ends, of length 25 cm if the speed of sound in air is 330 m/s.
Distinguish between an overtone and harmonic.
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).
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 open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their pth overtone is ______.
The fundamental frequency of sonometer wire increases by 9 Hz, if its tension is increased by 69%, keeping the length constant. The frequency of the wire is ______.
Length of an organ pipe open at both ends is 34 cm. If velocity of sound is 340 m is, then the frequency of 2nd overtone is ______.
An organ pipe has fundamental frequency 100 Hz. If its one end is closed, the frequencies produced will be ______.
If we study the vibration of a pipe open at both ends, then which of the following statements is not true?
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 ______
An organ pipe P1 closed at one end vibrating in its first overtone and another pipe P2 open at both ends vibrating in third overtone are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 is ______.
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 ______.
Two organ pipes are emitting their fundamental notes, when each closed at end, give 5 beats per sec. If their fundamental frequencies are 250 Hz and 255 Hz, then find the ratio of their lengths.
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 ______.
Two wires, each 1 m long and of the same diameter, have densities 8 × 103 kg/m3 and 2 × 103 kg/m3 and are stretched by tensions 196 N and 49 N respectively. Compare their fundamental frequencies.
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.)
In fundamental mode, the time required for the sound wave to reach up to closed end of a pipe filled with air is 't' second. The frequency of vibration of air column is (Neglect end correction) ______.
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 ______.
