Advertisements
Advertisements
प्रश्न
For the travelling harmonic wave
y (x, t) = 2.0 cos 2π (10t – 0.0080x + 0.35)
Where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of 4 m.
Advertisements
उत्तर १
Equation for a travelling harmonic wave is given as:
y (x, t) = 2.0 cos 2π (10t – 0.0080x + 0.35)
= 2.0 cos (20 π t – 0.016 π x + 0.70 π)
Where,
Propagation constant, k = 0.0160 π
Amplitude, a = 2 cm
Angular frequency, ω= 20 π rad/s
Phase difference is given by the relation:
`phi = "k"x = (2pi)/lambda`
For x = 4 m = 400 cm
Φ = 0.016 π × 400
= 6.4 π rad
उत्तर २
The given equation can be drawn be rewritten as under
`"y"(x, "t") = 2.0 cos [2pi (10"t" - 0.0080 x) + 2pi xx 0.35]`
or `"y"(x, "t") = 2.0 cos [2pi xx 0.0080((10"t")/0.0080 - x) + 0.7 pi]`
Comparing this equation with the standard equation of a travelling harmonic wave.
`(2pi)/lambda = 2pi xx 0.0080` or `lambda = 1/0.0080 " cm" = 125` cm
The phase difference between oscillatory motion of two points seperated by a distance `trianglex` is given by
`trianglephi = (2pi)/lambda trianglex`
When `triangle z = 4 m = 400` cm then
`trianglephi = (2pi)/125 xx 400`
`= 6.4 pi " rad"`
APPEARS IN
संबंधित प्रश्न
A stone dropped from the top of a tower of height 300 m high splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is 340 m s–1? (g= 9.8 m s–2)
A sine wave is travelling in a medium. The minimum distance between the two particles, always having same speed, is
Choose the correct option:
Which of the following equations represents a wave travelling along Y-axis?
Velocity of sound in air is 332 m s−1. Its velocity in vacuum will be
Two wave pulses travel in opposite directions on a string and approach each other. The shape of one pulse is inverted with respect to the other.
A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416. Hz. If the length is doubled keeping other things same, the string will ______.
A pulse travelling on a string is represented by the function \[y = \frac{a^2}{\left( x - \nu t \right)^2 + a^2},\] where a = 5 mm and ν = 20 cm-1. Sketch the shape of the string at t = 0, 1 s and 2 s. Take x = 0 in the middle of the string.
A string of length 40 cm and weighing 10 g is attached to a spring at one end and to a fixed wall at the other end. The spring has a spring constant of 160 N m−1 and is stretched by 1⋅0 cm. If a wave pulse is produced on the string near the wall, how much time will it take to reach the spring?
A 200 Hz wave with amplitude 1 mm travels on a long string of linear mass density 6 g m−1 kept under a tension of 60 N. (a) Find the average power transmitted across a given point on the string. (b) Find the total energy associated with the wave in a 2⋅0 m long portion of the string.
Following figure shows two wave pulses at t = 0 travelling on a string in opposite directions with the same wave speed 50 cm s−1. Sketch the shape of the string at t = 4 ms, 6 ms, 8 ms, and 12 ms.
A wire of length 2⋅00 m is stretched to a tension of 160 N. If the fundamental frequency of vibration is 100 Hz, find its linear mass density.
A steel wire fixed at both ends has a fundamental frequency of 200 Hz. A person can hear sound of maximum frequency 14 kHz. What is the highest harmonic that can be played on this string which is audible to the person?
The equation for the vibration of a string, fixed at both ends vibrating in its third harmonic, is given by
\[y = \left( 0 \cdot 4 cm \right) \sin\left[ \left( 0 \cdot 314 {cm}^{- 1} \right) x \right] \cos \left[ \left( 600\pi s^{- 1} \right) t \right]\]
(a) What is the frequency of vibration? (b) What are the positions of the nodes? (c) What is the length of the string? (d) What is the wavelength and the speed of two travelling waves that can interfere to give this vibration?
Use the formula `v = sqrt((gamma P)/rho)` to explain why the speed of sound in air is independent of pressure.
A bat emits an ultrasonic sound of frequency 1000 kHz in the air. If the sound meets a water surface, what is the wavelength of the the reflected sound? The speed of sound in air is 340 m s–1 and in water 1486 m s–1.
A sound wave is passing through air column in the form of compression and rarefaction. In consecutive compressions and rarefactions ______.
If c is r.m.s. speed of molecules in a gas and v is the speed of sound waves in the gas, show that c/v is constant and independent of temperature for all diatomic gases.
An engine is approaching a cliff at a constant speed. When it is at a distance of 0.9 km from cliff it sounds a whistle. The echo of the sound is heard by the driver after 5 seconds. Velocity of sound in air is equal to 330 ms-1. The speed of the engine is ______ km/h.
